diff --git a/pandas/_libs/tslibs/timestamps.pyx b/pandas/_libs/tslibs/timestamps.pyx
index 317dc769636fb..03ed26337d539 100644
--- a/pandas/_libs/tslibs/timestamps.pyx
+++ b/pandas/_libs/tslibs/timestamps.pyx
@@ -36,7 +36,6 @@ from pandas._libs.tslibs.tzconversion import (
 # Constants
 _zero_time = datetime_time(0, 0)
 _no_input = object()
-PY36 = sys.version_info >= (3, 6)
 
 # ----------------------------------------------------------------------
 
@@ -982,9 +981,8 @@ default 'raise'
         else:
             kwargs = {'year': dts.year, 'month': dts.month, 'day': dts.day,
                       'hour': dts.hour, 'minute': dts.min, 'second': dts.sec,
-                      'microsecond': dts.us, 'tzinfo': _tzinfo}
-            if PY36:
-                kwargs['fold'] = fold
+                      'microsecond': dts.us, 'tzinfo': _tzinfo,
+                      'fold': fold}
             ts_input = datetime(**kwargs)
 
         ts = convert_datetime_to_tsobject(ts_input, _tzinfo)
diff --git a/pandas/compat/__init__.py b/pandas/compat/__init__.py
index 890d0aca0019d..684fbbc23c86c 100644
--- a/pandas/compat/__init__.py
+++ b/pandas/compat/__init__.py
@@ -12,7 +12,6 @@
 import sys
 import warnings
 
-PY36 = sys.version_info >= (3, 6)
 PY37 = sys.version_info >= (3, 7)
 PY38 = sys.version_info >= (3, 8)
 PYPY = platform.python_implementation() == "PyPy"
diff --git a/pandas/core/common.py b/pandas/core/common.py
index 565f5076fdddb..133e60de5d694 100644
--- a/pandas/core/common.py
+++ b/pandas/core/common.py
@@ -5,7 +5,7 @@
 """
 
 import collections
-from collections import OrderedDict, abc
+from collections import abc
 from datetime import datetime, timedelta
 from functools import partial
 import inspect
@@ -14,7 +14,6 @@
 import numpy as np
 
 from pandas._libs import lib, tslibs
-from pandas.compat import PY36
 
 from pandas.core.dtypes.cast import construct_1d_object_array_from_listlike
 from pandas.core.dtypes.common import (
@@ -215,16 +214,6 @@ def try_sort(iterable):
         return listed
 
 
-def dict_keys_to_ordered_list(mapping):
-    # when pandas drops support for Python < 3.6, this function
-    # can be replaced by a simple list(mapping.keys())
-    if PY36 or isinstance(mapping, OrderedDict):
-        keys = list(mapping.keys())
-    else:
-        keys = try_sort(mapping)
-    return keys
-
-
 def asarray_tuplesafe(values, dtype=None):
 
     if not (isinstance(values, (list, tuple)) or hasattr(values, "__array__")):
diff --git a/pandas/core/dtypes/common.py b/pandas/core/dtypes/common.py
index 1ed54c12f4a34..635bc5ce03680 100644
--- a/pandas/core/dtypes/common.py
+++ b/pandas/core/dtypes/common.py
@@ -6,7 +6,6 @@
 
 from pandas._libs import algos, lib
 from pandas._libs.tslibs import conversion
-from pandas.compat import PY36
 
 from pandas.core.dtypes.dtypes import (
     CategoricalDtype,
@@ -1266,9 +1265,6 @@ def _is_unorderable_exception(e: TypeError) -> bool:
     """
     Check if the exception raised is an unorderable exception.
 
-    The error message differs for 3 <= PY <= 3.5 and PY >= 3.6, so
-    we need to condition based on Python version.
-
     Parameters
     ----------
     e : Exception or sub-class
@@ -1276,14 +1272,10 @@ def _is_unorderable_exception(e: TypeError) -> bool:
 
     Returns
     -------
-    boolean
+    bool
         Whether or not the exception raised is an unorderable exception.
     """
-
-    if PY36:
-        return "'>' not supported between instances of" in str(e)
-
-    return "unorderable" in str(e)
+    return "'>' not supported between instances of" in str(e)
 
 
 def needs_i8_conversion(arr_or_dtype) -> bool:
diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index ebee8b10896be..231f3bf56fc36 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -34,7 +34,6 @@
 from pandas._config import get_option
 
 from pandas._libs import algos as libalgos, lib
-from pandas.compat import PY36
 from pandas.compat.numpy import function as nv
 from pandas.util._decorators import (
     Appender,
@@ -3498,16 +3497,12 @@ def assign(self, **kwargs):
         Notes
         -----
         Assigning multiple columns within the same ``assign`` is possible.
-        For Python 3.6 and above, later items in '\*\*kwargs' may refer to
-        newly created or modified columns in 'df'; items are computed and
-        assigned into 'df' in order.  For Python 3.5 and below, the order of
-        keyword arguments is not specified, you cannot refer to newly created
-        or modified columns. All items are computed first, and then assigned
-        in alphabetical order.
+        Later items in '\*\*kwargs' may refer to newly created or modified
+        columns in 'df'; items are computed and assigned into 'df' in order.
 
         .. versionchanged:: 0.23.0
 
-           Keyword argument order is maintained for Python 3.6 and later.
+           Keyword argument order is maintained.
 
         Examples
         --------
@@ -3533,9 +3528,8 @@ def assign(self, **kwargs):
         Portland    17.0    62.6
         Berkeley    25.0    77.0
 
-        In Python 3.6+, you can create multiple columns within the same assign
-        where one of the columns depends on another one defined within the same
-        assign:
+        You can create multiple columns within the same assign where one
+        of the columns depends on another one defined within the same assign:
 
         >>> df.assign(temp_f=lambda x: x['temp_c'] * 9 / 5 + 32,
         ...           temp_k=lambda x: (x['temp_f'] +  459.67) * 5 / 9)
@@ -3545,21 +3539,8 @@ def assign(self, **kwargs):
         """
         data = self.copy()
 
-        # >= 3.6 preserve order of kwargs
-        if PY36:
-            for k, v in kwargs.items():
-                data[k] = com.apply_if_callable(v, data)
-        else:
-            # <= 3.5: do all calculations first...
-            results = OrderedDict()
-            for k, v in kwargs.items():
-                results[k] = com.apply_if_callable(v, data)
-
-            # <= 3.5 and earlier
-            results = sorted(results.items())
-            # ... and then assign
-            for k, v in results:
-                data[k] = v
+        for k, v in kwargs.items():
+            data[k] = com.apply_if_callable(v, data)
         return data
 
     def _sanitize_column(self, key, value, broadcast=True):
diff --git a/pandas/core/generic.py b/pandas/core/generic.py
index 1b892c02ba7bf..47a0582edbea4 100644
--- a/pandas/core/generic.py
+++ b/pandas/core/generic.py
@@ -8,7 +8,6 @@
 import re
 from textwrap import dedent
 from typing import (
-    TYPE_CHECKING,
     Any,
     Callable,
     Dict,
@@ -190,12 +189,7 @@ class NDFrame(PandasObject, SelectionMixin):
     _metadata = []  # type: List[str]
     _is_copy = None
     _data = None  # type: BlockManager
-
-    if TYPE_CHECKING:
-        # TODO(PY36): replace with _attrs : Dict[Hashable, Any]
-        # We need the TYPE_CHECKING, because _attrs is not a class attribute
-        # and Py35 doesn't support the new syntax.
-        _attrs = {}  # type: Dict[Optional[Hashable], Any]
+    _attrs: Dict[Optional[Hashable], Any]
 
     # ----------------------------------------------------------------------
     # Constructors
diff --git a/pandas/core/groupby/generic.py b/pandas/core/groupby/generic.py
index dda98d2dd438b..8f0b8a1e37af2 100644
--- a/pandas/core/groupby/generic.py
+++ b/pandas/core/groupby/generic.py
@@ -28,7 +28,6 @@
 import numpy as np
 
 from pandas._libs import Timestamp, lib
-from pandas.compat import PY36
 from pandas.util._decorators import Appender, Substitution
 
 from pandas.core.dtypes.cast import (
@@ -233,10 +232,6 @@ def aggregate(self, func=None, *args, **kwargs):
         no_arg_message = "Must provide 'func' or named aggregation **kwargs."
         if relabeling:
             columns = list(kwargs)
-            if not PY36:
-                # sort for 3.5 and earlier
-                columns = list(sorted(columns))
-
             func = [kwargs[col] for col in columns]
             kwargs = {}
             if not columns:
@@ -1804,9 +1799,6 @@ def _normalize_keyword_aggregation(kwargs):
     >>> _normalize_keyword_aggregation({'output': ('input', 'sum')})
     (OrderedDict([('input', ['sum'])]), ('output',), [('input', 'sum')])
     """
-    if not PY36:
-        kwargs = OrderedDict(sorted(kwargs.items()))
-
     # Normalize the aggregation functions as Dict[column, List[func]],
     # process normally, then fixup the names.
     # TODO(Py35): When we drop python 3.5, change this to
diff --git a/pandas/core/internals/construction.py b/pandas/core/internals/construction.py
index 05a2803b3fc2f..e4a6ca85ac05c 100644
--- a/pandas/core/internals/construction.py
+++ b/pandas/core/internals/construction.py
@@ -2,14 +2,12 @@
 Functions for preparing various inputs passed to the DataFrame or Series
 constructors before passing them to a BlockManager.
 """
-from collections import OrderedDict, abc
+from collections import abc
 
 import numpy as np
 import numpy.ma as ma
 
 from pandas._libs import lib
-import pandas.compat as compat
-from pandas.compat import PY36
 
 from pandas.core.dtypes.cast import (
     construct_1d_arraylike_from_scalar,
@@ -235,7 +233,7 @@ def init_dict(data, index, columns, dtype=None):
             arrays.loc[missing] = [val] * missing.sum()
 
     else:
-        keys = com.dict_keys_to_ordered_list(data)
+        keys = list(data.keys())
         columns = data_names = Index(keys)
         arrays = (com.maybe_iterable_to_list(data[k]) for k in keys)
         # GH#24096 need copy to be deep for datetime64tz case
@@ -331,7 +329,6 @@ def extract_index(data):
         have_raw_arrays = False
         have_series = False
         have_dicts = False
-        have_ordered = False
 
         for val in data:
             if isinstance(val, ABCSeries):
@@ -339,8 +336,6 @@ def extract_index(data):
                 indexes.append(val.index)
             elif isinstance(val, dict):
                 have_dicts = True
-                if isinstance(val, OrderedDict):
-                    have_ordered = True
                 indexes.append(list(val.keys()))
             elif is_list_like(val) and getattr(val, "ndim", 1) == 1:
                 have_raw_arrays = True
@@ -352,7 +347,7 @@ def extract_index(data):
         if have_series:
             index = _union_indexes(indexes)
         elif have_dicts:
-            index = _union_indexes(indexes, sort=not (compat.PY36 or have_ordered))
+            index = _union_indexes(indexes, sort=False)
 
         if have_raw_arrays:
             lengths = list(set(raw_lengths))
@@ -531,7 +526,7 @@ def _list_of_dict_to_arrays(data, columns, coerce_float=False, dtype=None):
     """Convert list of dicts to numpy arrays
 
     if `columns` is not passed, column names are inferred from the records
-    - for OrderedDict and (on Python>=3.6) dicts, the column names match
+    - for OrderedDict and dicts, the column names match
       the key insertion-order from the first record to the last.
     - For other kinds of dict-likes, the keys are lexically sorted.
 
@@ -550,8 +545,7 @@ def _list_of_dict_to_arrays(data, columns, coerce_float=False, dtype=None):
     """
     if columns is None:
         gen = (list(x.keys()) for x in data)
-        types = (dict, OrderedDict) if PY36 else OrderedDict
-        sort = not any(isinstance(d, types) for d in data)
+        sort = not any(isinstance(d, dict) for d in data)
         columns = lib.fast_unique_multiple_list_gen(gen, sort=sort)
 
     # assure that they are of the base dict class and not of derived
diff --git a/pandas/core/reshape/concat.py b/pandas/core/reshape/concat.py
index 772ac1cd93059..3c1b2b1eb11d2 100644
--- a/pandas/core/reshape/concat.py
+++ b/pandas/core/reshape/concat.py
@@ -293,7 +293,7 @@ def __init__(
 
         if isinstance(objs, dict):
             if keys is None:
-                keys = com.dict_keys_to_ordered_list(objs)
+                keys = list(objs.keys())
             objs = [objs[k] for k in keys]
         else:
             objs = list(objs)
diff --git a/pandas/core/series.py b/pandas/core/series.py
index 7327c2d543836..c5e639fef8c5b 100644
--- a/pandas/core/series.py
+++ b/pandas/core/series.py
@@ -1,7 +1,6 @@
 """
 Data structure for 1-dimensional cross-sectional and time series data
 """
-from collections import OrderedDict
 from io import StringIO
 from shutil import get_terminal_size
 from textwrap import dedent
@@ -13,7 +12,6 @@
 from pandas._config import get_option
 
 from pandas._libs import index as libindex, lib, reshape, tslibs
-from pandas.compat import PY36
 from pandas.compat.numpy import function as nv
 from pandas.util._decorators import Appender, Substitution, deprecate
 from pandas.util._validators import validate_bool_kwarg, validate_percentile
@@ -364,13 +362,6 @@ def _init_dict(self, data, index=None, dtype=None):
         # Now we just make sure the order is respected, if any
         if data and index is not None:
             s = s.reindex(index, copy=False)
-        elif not PY36 and not isinstance(data, OrderedDict) and data:
-            # Need the `and data` to avoid sorting Series(None, index=[...])
-            # since that isn't really dict-like
-            try:
-                s = s.sort_index()
-            except TypeError:
-                pass
         return s._data, s.index
 
     @classmethod
diff --git a/pandas/io/pickle.py b/pandas/io/pickle.py
index 5e066c4f9ecbd..0a0ccedd78f00 100644
--- a/pandas/io/pickle.py
+++ b/pandas/io/pickle.py
@@ -2,7 +2,7 @@
 import pickle
 import warnings
 
-from pandas.compat import PY36, pickle_compat as pc
+from pandas.compat import pickle_compat as pc
 
 from pandas.io.common import _get_handle, _stringify_path
 
@@ -140,9 +140,7 @@ def read_pickle(path, compression="infer"):
     # 1) try standard library Pickle
     # 2) try pickle_compat (older pandas version) to handle subclass changes
 
-    excs_to_catch = (AttributeError, ImportError)
-    if PY36:
-        excs_to_catch += (ModuleNotFoundError,)
+    excs_to_catch = (AttributeError, ImportError, ModuleNotFoundError)
 
     try:
         with warnings.catch_warnings(record=True):
diff --git a/pandas/tests/extension/json/test_json.py b/pandas/tests/extension/json/test_json.py
index bc75ec6aeb2df..7e027a65eec3a 100644
--- a/pandas/tests/extension/json/test_json.py
+++ b/pandas/tests/extension/json/test_json.py
@@ -3,8 +3,6 @@
 
 import pytest
 
-from pandas.compat import PY36
-
 import pandas as pd
 from pandas.tests.extension import base
 import pandas.util.testing as tm
@@ -180,9 +178,6 @@ def test_fillna_frame(self):
 
 
 unhashable = pytest.mark.skip(reason="Unhashable")
-unstable = pytest.mark.skipif(
-    not PY36, reason="Dictionary order unstable"  # 3.6 or higher
-)
 
 
 class TestReduce(base.BaseNoReduceTests):
@@ -199,20 +194,16 @@ def test_sort_values_frame(self):
         # TODO (EA.factorize): see if _values_for_factorize allows this.
         pass
 
-    @unstable
     def test_argsort(self, data_for_sorting):
         super().test_argsort(data_for_sorting)
 
-    @unstable
     def test_argsort_missing(self, data_missing_for_sorting):
         super().test_argsort_missing(data_missing_for_sorting)
 
-    @unstable
     @pytest.mark.parametrize("ascending", [True, False])
     def test_sort_values(self, data_for_sorting, ascending):
         super().test_sort_values(data_for_sorting, ascending)
 
-    @unstable
     @pytest.mark.parametrize("ascending", [True, False])
     def test_sort_values_missing(self, data_missing_for_sorting, ascending):
         super().test_sort_values_missing(data_missing_for_sorting, ascending)
@@ -280,7 +271,6 @@ def test_groupby_extension_apply(self):
         we'll be able to dispatch unique.
         """
 
-    @unstable
     @pytest.mark.parametrize("as_index", [True, False])
     def test_groupby_extension_agg(self, as_index, data_for_grouping):
         super().test_groupby_extension_agg(as_index, data_for_grouping)
diff --git a/pandas/tests/frame/test_constructors.py b/pandas/tests/frame/test_constructors.py
index 1d030bbc75521..77a7783deeee3 100644
--- a/pandas/tests/frame/test_constructors.py
+++ b/pandas/tests/frame/test_constructors.py
@@ -8,7 +8,7 @@
 import numpy.ma.mrecords as mrecords
 import pytest
 
-from pandas.compat import PY36, is_platform_little_endian
+from pandas.compat import is_platform_little_endian
 
 from pandas.core.dtypes.cast import construct_1d_object_array_from_listlike
 from pandas.core.dtypes.common import is_integer_dtype
@@ -387,7 +387,6 @@ def test_constructor_dict_nan_tuple_key(self, value):
         result = DataFrame(data, index=idx, columns=cols)
         tm.assert_frame_equal(result, expected)
 
-    @pytest.mark.skipif(not PY36, reason="Insertion order for Python>=3.6")
     def test_constructor_dict_order_insertion(self):
         datetime_series = tm.makeTimeSeries(nper=30)
         datetime_series_short = tm.makeTimeSeries(nper=25)
@@ -399,18 +398,6 @@ def test_constructor_dict_order_insertion(self):
         expected = DataFrame(data=d, columns=list("ba"))
         tm.assert_frame_equal(frame, expected)
 
-    @pytest.mark.skipif(PY36, reason="order by value for Python<3.6")
-    def test_constructor_dict_order_by_values(self):
-        datetime_series = tm.makeTimeSeries(nper=30)
-        datetime_series_short = tm.makeTimeSeries(nper=25)
-
-        # GH19018
-        # initialization ordering: by value if python<3.6
-        d = {"b": datetime_series_short, "a": datetime_series}
-        frame = DataFrame(data=d)
-        expected = DataFrame(data=d, columns=list("ab"))
-        tm.assert_frame_equal(frame, expected)
-
     def test_constructor_multi_index(self):
         # GH 4078
         # construction error with mi and all-nan frame
@@ -1373,7 +1360,7 @@ def test_constructor_list_of_dict_order(self):
             }
         )
         result = DataFrame(data)
-        tm.assert_frame_equal(result, expected, check_like=not PY36)
+        tm.assert_frame_equal(result, expected)
 
     def test_constructor_orient(self, float_string_frame):
         data_dict = float_string_frame.T._series
diff --git a/pandas/tests/frame/test_mutate_columns.py b/pandas/tests/frame/test_mutate_columns.py
index 7feb55f2fac09..8c0dd67af4e7d 100644
--- a/pandas/tests/frame/test_mutate_columns.py
+++ b/pandas/tests/frame/test_mutate_columns.py
@@ -3,8 +3,6 @@
 import numpy as np
 import pytest
 
-from pandas.compat import PY36
-
 from pandas import DataFrame, Index, MultiIndex, Series
 import pandas.util.testing as tm
 
@@ -60,10 +58,7 @@ def test_assign_order(self):
         df = DataFrame([[1, 2], [3, 4]], columns=["A", "B"])
         result = df.assign(D=df.A + df.B, C=df.A - df.B)
 
-        if PY36:
-            expected = DataFrame([[1, 2, 3, -1], [3, 4, 7, -1]], columns=list("ABDC"))
-        else:
-            expected = DataFrame([[1, 2, -1, 3], [3, 4, -1, 7]], columns=list("ABCD"))
+        expected = DataFrame([[1, 2, 3, -1], [3, 4, 7, -1]], columns=list("ABDC"))
         tm.assert_frame_equal(result, expected)
         result = df.assign(C=df.A - df.B, D=df.A + df.B)
 
@@ -80,25 +75,6 @@ def test_assign_bad(self):
         with pytest.raises(AttributeError):
             df.assign(C=df.A, D=df.A + df.C)
 
-    @pytest.mark.skipif(
-        PY36,
-        reason="""Issue #14207: valid for python
-                        3.6 and above""",
-    )
-    def test_assign_dependent_old_python(self):
-        df = DataFrame({"A": [1, 2, 3], "B": [4, 5, 6]})
-
-        # Key C does not exist at definition time of df
-        with pytest.raises(KeyError, match="^'C'$"):
-            df.assign(C=lambda df: df.A, D=lambda df: df["A"] + df["C"])
-        with pytest.raises(KeyError, match="^'C'$"):
-            df.assign(C=df.A, D=lambda x: x["A"] + x["C"])
-
-    @pytest.mark.skipif(
-        not PY36,
-        reason="""Issue #14207: not valid for
-                        python 3.5 and below""",
-    )
     def test_assign_dependent(self):
         df = DataFrame({"A": [1, 2], "B": [3, 4]})
 
diff --git a/pandas/tests/groupby/aggregate/test_aggregate.py b/pandas/tests/groupby/aggregate/test_aggregate.py
index c03ffe317083c..a478bf19d0f10 100644
--- a/pandas/tests/groupby/aggregate/test_aggregate.py
+++ b/pandas/tests/groupby/aggregate/test_aggregate.py
@@ -8,7 +8,7 @@
 import pytest
 
 import pandas as pd
-from pandas import DataFrame, Index, MultiIndex, Series, compat, concat
+from pandas import DataFrame, Index, MultiIndex, Series, concat
 from pandas.core.base import SpecificationError
 from pandas.core.groupby.generic import _make_unique, _maybe_mangle_lambdas
 from pandas.core.groupby.grouper import Grouping
@@ -361,9 +361,7 @@ def test_series_named_agg(self):
         tm.assert_frame_equal(result, expected)
 
         result = gr.agg(b="min", a="sum")
-        # sort for 35 and earlier
-        if compat.PY36:
-            expected = expected[["b", "a"]]
+        expected = expected[["b", "a"]]
         tm.assert_frame_equal(result, expected)
 
     def test_no_args_raises(self):
@@ -425,8 +423,6 @@ def test_agg_relabel(self):
             index=pd.Index(["a", "b"], name="group"),
             columns=["b_min", "a_min", "a_mean", "a_max", "b_max", "a_98"],
         )
-        if not compat.PY36:
-            expected = expected[["a_98", "a_max", "a_mean", "a_min", "b_max", "b_min"]]
         tm.assert_frame_equal(result, expected)
 
     def test_agg_relabel_non_identifier(self):
diff --git a/pandas/tests/indexes/test_base.py b/pandas/tests/indexes/test_base.py
index e43d340a46d9f..fe9953341fdae 100644
--- a/pandas/tests/indexes/test_base.py
+++ b/pandas/tests/indexes/test_base.py
@@ -11,7 +11,6 @@
 import pandas._config.config as cf
 
 from pandas._libs.tslib import Timestamp
-from pandas.compat import PY36
 from pandas.compat.numpy import np_datetime64_compat
 
 from pandas.core.dtypes.common import is_unsigned_integer_dtype
@@ -1616,11 +1615,7 @@ def test_get_loc(self, method):
     def test_get_loc_raises_bad_label(self, method):
         index = pd.Index([0, 1, 2])
         if method:
-            # Messages vary across versions
-            if PY36:
-                msg = "not supported between"
-            else:
-                msg = "unorderable types"
+            msg = "not supported between"
         else:
             msg = "invalid key"
 
@@ -2444,21 +2439,13 @@ def create_index(self):
 
     def test_argsort(self):
         index = self.create_index()
-        if PY36:
-            with pytest.raises(TypeError, match="'>|<' not supported"):
-                index.argsort()
-        else:
-            with pytest.raises(TypeError, match="unorderable types"):
-                index.argsort()
+        with pytest.raises(TypeError, match="'>|<' not supported"):
+            index.argsort()
 
     def test_numpy_argsort(self):
         index = self.create_index()
-        if PY36:
-            with pytest.raises(TypeError, match="'>|<' not supported"):
-                np.argsort(index)
-        else:
-            with pytest.raises(TypeError, match="unorderable types"):
-                np.argsort(index)
+        with pytest.raises(TypeError, match="'>|<' not supported"):
+            np.argsort(index)
 
     def test_copy_name(self):
         # Check that "name" argument passed at initialization is honoured
diff --git a/pandas/tests/indexing/test_indexing.py b/pandas/tests/indexing/test_indexing.py
index d6d3763981131..fc5753ec2955c 100644
--- a/pandas/tests/indexing/test_indexing.py
+++ b/pandas/tests/indexing/test_indexing.py
@@ -7,7 +7,6 @@
 import numpy as np
 import pytest
 
-from pandas.compat import PY36
 from pandas.errors import AbstractMethodError
 
 from pandas.core.dtypes.common import is_float_dtype, is_integer_dtype
@@ -222,7 +221,7 @@ def test_setitem_dtype_upcast(self):
         expected = DataFrame(
             [{"a": 1, "b": np.nan, "c": "foo"}, {"a": 3, "b": 2, "c": np.nan}]
         )
-        tm.assert_frame_equal(df, expected, check_like=not PY36)
+        tm.assert_frame_equal(df, expected)
 
         # GH10280
         df = DataFrame(
diff --git a/pandas/tests/internals/test_internals.py b/pandas/tests/internals/test_internals.py
index ee7fca6ec7672..fa7a98c617677 100644
--- a/pandas/tests/internals/test_internals.py
+++ b/pandas/tests/internals/test_internals.py
@@ -1,10 +1,8 @@
 from collections import OrderedDict
 from datetime import date, datetime
-from distutils.version import LooseVersion
 import itertools
 import operator
 import re
-import sys
 
 import numpy as np
 import pytest
@@ -26,9 +24,6 @@
 from pandas.core.internals import BlockManager, SingleBlockManager, make_block
 import pandas.util.testing as tm
 
-# in 3.6.1 a c-api slicing function changed, see src/compat_helper.h
-PY361 = LooseVersion(sys.version) >= LooseVersion("3.6.1")
-
 
 @pytest.fixture
 def mgr():
@@ -1096,10 +1091,6 @@ def assert_as_slice_equals(arr, slc):
 
         assert_as_slice_equals([2, 1], slice(2, 0, -1))
 
-        if not PY361:
-            assert_as_slice_equals([2, 1, 0], slice(2, None, -1))
-            assert_as_slice_equals([100, 0], slice(100, None, -100))
-
     def test_not_slice_like_arrays(self):
         def assert_not_slice_like(arr):
             assert not BlockPlacement(arr).is_slice_like
@@ -1119,10 +1110,6 @@ def test_slice_iter(self):
         assert list(BlockPlacement(slice(0, 0))) == []
         assert list(BlockPlacement(slice(3, 0))) == []
 
-        if not PY361:
-            assert list(BlockPlacement(slice(3, 0, -1))) == [3, 2, 1]
-            assert list(BlockPlacement(slice(3, None, -1))) == [3, 2, 1, 0]
-
     def test_slice_to_array_conversion(self):
         def assert_as_array_equals(slc, asarray):
             tm.assert_numpy_array_equal(
@@ -1135,10 +1122,6 @@ def assert_as_array_equals(slc, asarray):
 
         assert_as_array_equals(slice(3, 0, -1), [3, 2, 1])
 
-        if not PY361:
-            assert_as_array_equals(slice(3, None, -1), [3, 2, 1, 0])
-            assert_as_array_equals(slice(31, None, -10), [31, 21, 11, 1])
-
     def test_blockplacement_add(self):
         bpl = BlockPlacement(slice(0, 5))
         assert bpl.add(1).as_slice == slice(1, 6, 1)
@@ -1168,14 +1151,6 @@ def assert_add_equals(val, inc, result):
         with pytest.raises(ValueError):
             BlockPlacement([1, 2, 4]).add(-10)
 
-        if not PY361:
-            assert_add_equals(slice(3, 0, -1), -1, [2, 1, 0])
-            assert_add_equals(slice(2, None, -1), 0, [2, 1, 0])
-            assert_add_equals(slice(2, None, -1), 10, [12, 11, 10])
-
-            with pytest.raises(ValueError):
-                BlockPlacement(slice(2, None, -1)).add(-1)
-
 
 class DummyElement:
     def __init__(self, value, dtype):
diff --git a/pandas/tests/io/excel/test_writers.py b/pandas/tests/io/excel/test_writers.py
index 1bc4ad3e7867a..a7730e079a1bb 100644
--- a/pandas/tests/io/excel/test_writers.py
+++ b/pandas/tests/io/excel/test_writers.py
@@ -6,7 +6,6 @@
 import numpy as np
 import pytest
 
-from pandas.compat import PY36
 import pandas.util._test_decorators as td
 
 import pandas as pd
@@ -1262,7 +1261,6 @@ def check_called(func):
 
 @td.skip_if_no("xlrd")
 @td.skip_if_no("openpyxl")
-@pytest.mark.skipif(not PY36, reason="requires fspath")
 class TestFSPath:
     def test_excelfile_fspath(self):
         with tm.ensure_clean("foo.xlsx") as path:
diff --git a/pandas/tests/io/formats/test_format.py b/pandas/tests/io/formats/test_format.py
index 704de378b0909..0f4a7a33dd115 100644
--- a/pandas/tests/io/formats/test_format.py
+++ b/pandas/tests/io/formats/test_format.py
@@ -18,7 +18,7 @@
 import pytest
 import pytz
 
-from pandas.compat import PY36, is_platform_32bit, is_platform_windows
+from pandas.compat import is_platform_32bit, is_platform_windows
 
 import pandas as pd
 from pandas import (
@@ -62,10 +62,7 @@ def filepath_or_buffer(filepath_or_buffer_id, tmp_path):
         yield buf
         assert not buf.closed
     else:
-        if PY36:
-            assert isinstance(tmp_path, Path)
-        else:
-            assert hasattr(tmp_path, "__fspath__")
+        assert isinstance(tmp_path, Path)
         if filepath_or_buffer_id == "pathlike":
             yield tmp_path / "foo"
         else:
diff --git a/pandas/tests/io/json/test_normalize.py b/pandas/tests/io/json/test_normalize.py
index a3ca61cb1eb63..c71c52bce87b8 100644
--- a/pandas/tests/io/json/test_normalize.py
+++ b/pandas/tests/io/json/test_normalize.py
@@ -3,8 +3,6 @@
 import numpy as np
 import pytest
 
-from pandas.compat import PY36
-
 from pandas import DataFrame, Index
 import pandas.util.testing as tm
 
@@ -382,7 +380,7 @@ def test_missing_field(self, author_missing_data):
             },
         ]
         expected = DataFrame(ex_data)
-        tm.assert_frame_equal(result, expected, check_like=not PY36)
+        tm.assert_frame_equal(result, expected)
 
     @pytest.mark.parametrize(
         "max_level,expected",
@@ -524,7 +522,7 @@ def test_missing_meta(self, missing_metadata):
         columns = ["city", "number", "state", "street", "zip", "name"]
         columns = ["number", "street", "city", "state", "zip", "name"]
         expected = DataFrame(ex_data, columns=columns)
-        tm.assert_frame_equal(result, expected, check_like=not PY36)
+        tm.assert_frame_equal(result, expected)
 
     def test_donot_drop_nonevalues(self):
         # GH21356
diff --git a/pandas/tests/io/parser/test_common.py b/pandas/tests/io/parser/test_common.py
index 6e6c31bc5b972..590f26a76802a 100644
--- a/pandas/tests/io/parser/test_common.py
+++ b/pandas/tests/io/parser/test_common.py
@@ -2160,10 +2160,6 @@ def test_suppress_error_output(all_parsers, capsys):
     assert captured.err == ""
 
 
-@pytest.mark.skipif(
-    compat.is_platform_windows() and not compat.PY36,
-    reason="On Python < 3.6 won't pass on Windows",
-)
 @pytest.mark.parametrize("filename", ["sé-es-vé.csv", "ru-sй.csv", "中文文件名.csv"])
 def test_filename_with_special_chars(all_parsers, filename):
     # see gh-15086.
diff --git a/pandas/tests/io/pytables/test_store.py b/pandas/tests/io/pytables/test_store.py
index f9d525399bde3..a43da75005a65 100644
--- a/pandas/tests/io/pytables/test_store.py
+++ b/pandas/tests/io/pytables/test_store.py
@@ -9,7 +9,7 @@
 import numpy as np
 import pytest
 
-from pandas.compat import PY36, is_platform_little_endian, is_platform_windows
+from pandas.compat import is_platform_little_endian, is_platform_windows
 import pandas.util._test_decorators as td
 
 from pandas.core.dtypes.common import is_categorical_dtype
@@ -4711,7 +4711,6 @@ def test_read_hdf_series_mode_r(self, format, setup_path):
             result = pd.read_hdf(path, key="data", mode="r")
         tm.assert_series_equal(result, series)
 
-    @pytest.mark.skipif(not PY36, reason="Need python 3.6")
     def test_fspath(self):
         with tm.ensure_clean("foo.h5") as path:
             with pd.HDFStore(path) as store:
diff --git a/pandas/tests/reshape/test_concat.py b/pandas/tests/reshape/test_concat.py
index 46dafbc4e1ec8..323b3126c2461 100644
--- a/pandas/tests/reshape/test_concat.py
+++ b/pandas/tests/reshape/test_concat.py
@@ -27,7 +27,6 @@
     isna,
     read_csv,
 )
-import pandas.core.common as com
 from pandas.tests.extension.decimal import to_decimal
 import pandas.util.testing as tm
 
@@ -1264,7 +1263,7 @@ def test_concat_dict(self):
             "qux": DataFrame(np.random.randn(4, 3)),
         }
 
-        sorted_keys = com.dict_keys_to_ordered_list(frames)
+        sorted_keys = list(frames.keys())
 
         result = concat(frames)
         expected = concat([frames[k] for k in sorted_keys], keys=sorted_keys)
diff --git a/pandas/tests/scalar/timestamp/test_unary_ops.py b/pandas/tests/scalar/timestamp/test_unary_ops.py
index dffb957b8f3b0..db63e0bf9cd30 100644
--- a/pandas/tests/scalar/timestamp/test_unary_ops.py
+++ b/pandas/tests/scalar/timestamp/test_unary_ops.py
@@ -7,7 +7,6 @@
 
 from pandas._libs.tslibs import conversion
 from pandas._libs.tslibs.frequencies import INVALID_FREQ_ERR_MSG
-from pandas.compat import PY36
 import pandas.util._test_decorators as td
 
 from pandas import NaT, Timestamp
@@ -375,7 +374,6 @@ def test_replace_dst_border(self):
         expected = Timestamp("2013-11-3 03:00:00", tz="America/Chicago")
         assert result == expected
 
-    @pytest.mark.skipif(not PY36, reason="Fold not available until PY3.6")
     @pytest.mark.parametrize("fold", [0, 1])
     @pytest.mark.parametrize("tz", ["dateutil/Europe/London", "Europe/London"])
     def test_replace_dst_fold(self, fold, tz):
diff --git a/pandas/tests/series/test_constructors.py b/pandas/tests/series/test_constructors.py
index 4cbade2669cc6..34b11a0d008aa 100644
--- a/pandas/tests/series/test_constructors.py
+++ b/pandas/tests/series/test_constructors.py
@@ -7,7 +7,6 @@
 
 from pandas._libs import lib
 from pandas._libs.tslib import iNaT
-from pandas.compat import PY36
 
 from pandas.core.dtypes.common import is_categorical_dtype, is_datetime64tz_dtype
 from pandas.core.dtypes.dtypes import CategoricalDtype, ordered_sentinel
@@ -1048,10 +1047,7 @@ def test_constructor_dict_order(self):
         # order by value
         d = {"b": 1, "a": 0, "c": 2}
         result = Series(d)
-        if PY36:
-            expected = Series([1, 0, 2], index=list("bac"))
-        else:
-            expected = Series([0, 1, 2], index=list("abc"))
+        expected = Series([1, 0, 2], index=list("bac"))
         tm.assert_series_equal(result, expected)
 
     @pytest.mark.parametrize("value", [2, np.nan, None, float("nan")])
diff --git a/pandas/tests/test_downstream.py b/pandas/tests/test_downstream.py
index fb0511f8902f7..dc88ebe1f7f8e 100644
--- a/pandas/tests/test_downstream.py
+++ b/pandas/tests/test_downstream.py
@@ -8,8 +8,6 @@
 import numpy as np  # noqa
 import pytest
 
-from pandas.compat import PY36
-
 from pandas import DataFrame, Series
 import pandas.util.testing as tm
 
@@ -18,19 +16,10 @@ def import_module(name):
     # we *only* want to skip if the module is truly not available
     # and NOT just an actual import error because of pandas changes
 
-    if PY36:
-        try:
-            return importlib.import_module(name)
-        except ModuleNotFoundError:  # noqa
-            pytest.skip("skipping as {} not available".format(name))
-
-    else:
-        try:
-            return importlib.import_module(name)
-        except ImportError as e:
-            if "No module named" in str(e) and name in str(e):
-                pytest.skip("skipping as {} not available".format(name))
-            raise
+    try:
+        return importlib.import_module(name)
+    except ModuleNotFoundError:  # noqa
+        pytest.skip("skipping as {} not available".format(name))
 
 
 @pytest.fixture