diff --git a/doc/source/whatsnew/v1.2.0.rst b/doc/source/whatsnew/v1.2.0.rst
index 6f046d3a9379d..f9e348b04e318 100644
--- a/doc/source/whatsnew/v1.2.0.rst
+++ b/doc/source/whatsnew/v1.2.0.rst
@@ -727,6 +727,8 @@ Reshaping
 - Bug in :meth:`DataFrame.pivot_table` with ``aggfunc='count'`` or ``aggfunc='sum'`` returning ``NaN`` for missing categories when pivoted on a ``Categorical``. Now returning ``0`` (:issue:`31422`)
 - Bug in :func:`concat` and :class:`DataFrame` constructor where input index names are not preserved in some cases (:issue:`13475`)
 - Bug in func :meth:`crosstab` when using multiple columns with ``margins=True`` and ``normalize=True`` (:issue:`35144`)
+- Bug in :meth:`DataFrame.stack` where an empty DataFrame.stack would raise an error (:issue:`36113`). Now returning an empty Series with empty MultiIndex.
+- Bug in :meth:`Series.unstack`. Now a Series with single level of Index trying to unstack would raise a ValueError. (:issue:`36113`)
 - Bug in :meth:`DataFrame.agg` with ``func={'name':<FUNC>}`` incorrectly raising ``TypeError`` when ``DataFrame.columns==['Name']`` (:issue:`36212`)
 - Bug in :meth:`Series.transform` would give incorrect results or raise when the argument ``func`` was a dictionary (:issue:`35811`)
 - Bug in :meth:`DataFrame.pivot` did not preserve :class:`MultiIndex` level names for columns when rows and columns are both multiindexed (:issue:`36360`)
diff --git a/pandas/core/reshape/reshape.py b/pandas/core/reshape/reshape.py
index 44e165b2d06ee..c197e142fecbc 100644
--- a/pandas/core/reshape/reshape.py
+++ b/pandas/core/reshape/reshape.py
@@ -399,6 +399,7 @@ def _unstack_multiple(data, clocs, fill_value=None):
 
 
 def unstack(obj, level, fill_value=None):
+
     if isinstance(level, (tuple, list)):
         if len(level) != 1:
             # _unstack_multiple only handles MultiIndexes,
@@ -416,6 +417,13 @@ def unstack(obj, level, fill_value=None):
             return _unstack_frame(obj, level, fill_value=fill_value)
         else:
             return obj.T.stack(dropna=False)
+    elif not isinstance(obj.index, MultiIndex):
+        # GH 36113
+        # Give nicer error messages when unstack a  Series whose
+        # Index is not a MultiIndex.
+        raise ValueError(
+            f"index must be a MultiIndex to unstack, {type(obj.index)} was passed"
+        )
     else:
         if is_extension_array_dtype(obj.dtype):
             return _unstack_extension_series(obj, level, fill_value)
@@ -513,7 +521,7 @@ def factorize(index):
             verify_integrity=False,
         )
 
-    if frame._is_homogeneous_type:
+    if not frame.empty and frame._is_homogeneous_type:
         # For homogeneous EAs, frame._values will coerce to object. So
         # we concatenate instead.
         dtypes = list(frame.dtypes._values)
diff --git a/pandas/core/sorting.py b/pandas/core/sorting.py
index 2a0da8b0fb35c..729f517c789a7 100644
--- a/pandas/core/sorting.py
+++ b/pandas/core/sorting.py
@@ -610,7 +610,7 @@ def compress_group_index(group_index, sort: bool = True):
     if sort and len(obs_group_ids) > 0:
         obs_group_ids, comp_ids = _reorder_by_uniques(obs_group_ids, comp_ids)
 
-    return comp_ids, obs_group_ids
+    return ensure_int64(comp_ids), ensure_int64(obs_group_ids)
 
 
 def _reorder_by_uniques(uniques, labels):
diff --git a/pandas/tests/frame/test_stack_unstack.py b/pandas/tests/frame/test_stack_unstack.py
index 3fa17c1764de3..c70bfc4a3602b 100644
--- a/pandas/tests/frame/test_stack_unstack.py
+++ b/pandas/tests/frame/test_stack_unstack.py
@@ -1175,6 +1175,32 @@ def test_stack_timezone_aware_values():
     tm.assert_series_equal(result, expected)
 
 
+@pytest.mark.parametrize("dropna", [True, False])
+def test_stack_empty_frame(dropna):
+    # GH 36113
+    expected = Series(index=MultiIndex([[], []], [[], []]), dtype=np.float64)
+    result = DataFrame(dtype=np.float64).stack(dropna=dropna)
+    tm.assert_series_equal(result, expected)
+
+
+@pytest.mark.parametrize("dropna", [True, False])
+@pytest.mark.parametrize("fill_value", [None, 0])
+def test_stack_unstack_empty_frame(dropna, fill_value):
+    # GH 36113
+    result = (
+        DataFrame(dtype=np.int64).stack(dropna=dropna).unstack(fill_value=fill_value)
+    )
+    expected = DataFrame(dtype=np.int64)
+    tm.assert_frame_equal(result, expected)
+
+
+def test_unstack_single_index_series():
+    # GH 36113
+    msg = r"index must be a MultiIndex to unstack.*"
+    with pytest.raises(ValueError, match=msg):
+        Series(dtype=np.int64).unstack()
+
+
 def test_unstacking_multi_index_df():
     # see gh-30740
     df = DataFrame(
diff --git a/pandas/tests/reshape/test_pivot.py b/pandas/tests/reshape/test_pivot.py
index 5a28cd5c418f0..f9b2a02920841 100644
--- a/pandas/tests/reshape/test_pivot.py
+++ b/pandas/tests/reshape/test_pivot.py
@@ -4,8 +4,6 @@
 import numpy as np
 import pytest
 
-from pandas.compat import IS64
-
 import pandas as pd
 from pandas import (
     Categorical,
@@ -2102,7 +2100,6 @@ def test_pivot_duplicates(self):
         with pytest.raises(ValueError, match="duplicate entries"):
             data.pivot("a", "b", "c")
 
-    @pytest.mark.xfail(not IS64, reason="GH 36579: fail on 32-bit system")
     def test_pivot_empty(self):
         df = DataFrame(columns=["a", "b", "c"])
         result = df.pivot("a", "b", "c")