diff --git a/ci/deps/azure-36-minimum_versions.yaml b/ci/deps/azure-36-minimum_versions.yaml
index ae8fffa59fd50..f5af7bcf36189 100644
--- a/ci/deps/azure-36-minimum_versions.yaml
+++ b/ci/deps/azure-36-minimum_versions.yaml
@@ -1,6 +1,5 @@
 name: pandas-dev
 channels:
-  - defaults
   - conda-forge
 dependencies:
   - python=3.6.1
@@ -19,12 +18,12 @@ dependencies:
   - jinja2=2.8
   - numba=0.46.0
   - numexpr=2.6.2
-  - numpy=1.13.3
+  - numpy=1.15.4
   - openpyxl=2.5.7
   - pytables=3.4.3
   - python-dateutil=2.7.3
   - pytz=2017.2
-  - scipy=0.19.0
+  - scipy=1.2
   - xlrd=1.1.0
   - xlsxwriter=0.9.8
   - xlwt=1.2.0
diff --git a/ci/deps/azure-macos-36.yaml b/ci/deps/azure-macos-36.yaml
index 93885afbc4114..eeea249a19ca1 100644
--- a/ci/deps/azure-macos-36.yaml
+++ b/ci/deps/azure-macos-36.yaml
@@ -19,7 +19,7 @@ dependencies:
   - matplotlib=2.2.3
   - nomkl
   - numexpr
-  - numpy=1.14
+  - numpy=1.15.4
   - openpyxl
   - pyarrow>=0.13.0
   - pytables
diff --git a/conda.recipe/meta.yaml b/conda.recipe/meta.yaml
index 47f63c11d0567..e833ea1f1f398 100644
--- a/conda.recipe/meta.yaml
+++ b/conda.recipe/meta.yaml
@@ -20,12 +20,12 @@ requirements:
     - cython
     - numpy
     - setuptools >=3.3
-    - python-dateutil >=2.5.0
+    - python-dateutil >=2.7.3
     - pytz
   run:
     - python {{ python }}
     - {{ pin_compatible('numpy') }}
-    - python-dateutil >=2.5.0
+    - python-dateutil >=2.7.3
     - pytz
 
 test:
diff --git a/doc/source/getting_started/install.rst b/doc/source/getting_started/install.rst
index d392e151e3f97..ba99aaa9f430c 100644
--- a/doc/source/getting_started/install.rst
+++ b/doc/source/getting_started/install.rst
@@ -220,7 +220,7 @@ Dependencies
 Package                                                          Minimum supported version
 ================================================================ ==========================
 `setuptools <https://setuptools.readthedocs.io/en/latest/>`__    24.2.0
-`NumPy <https://www.numpy.org>`__                                1.13.3
+`NumPy <https://www.numpy.org>`__                                1.15.4
 `python-dateutil <https://dateutil.readthedocs.io/en/stable/>`__ 2.7.3
 `pytz <https://pypi.org/project/pytz/>`__                        2017.2
 ================================================================ ==========================
diff --git a/doc/source/whatsnew/v1.1.0.rst b/doc/source/whatsnew/v1.1.0.rst
index 40adeb28d47b6..26aee8133a1e9 100644
--- a/doc/source/whatsnew/v1.1.0.rst
+++ b/doc/source/whatsnew/v1.1.0.rst
@@ -157,13 +157,23 @@ Other enhancements
 Increased minimum versions for dependencies
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
 
-Some minimum supported versions of dependencies were updated (:issue:`29766`, :issue:`29723`, pytables >= 3.4.3).
+Some minimum supported versions of dependencies were updated (:issue:`33718`, :issue:`29766`, :issue:`29723`, pytables >= 3.4.3).
 If installed, we now require:
 
 +-----------------+-----------------+----------+---------+
 | Package         | Minimum Version | Required | Changed |
 +=================+=================+==========+=========+
-| python-dateutil | 2.7.3           |    X     |         |
+| numpy           | 1.15.4          |    X     |    X    |
++-----------------+-----------------+----------+---------+
+| pytz            | 2015.4          |    X     |         |
++-----------------+-----------------+----------+---------+
+| python-dateutil | 2.7.3           |    X     |    X    |
++-----------------+-----------------+----------+---------+
+| bottleneck      | 1.2.1           |          |         |
++-----------------+-----------------+----------+---------+
+| numexpr         | 2.6.2           |          |         |
++-----------------+-----------------+----------+---------+
+| pytest (dev)    | 4.0.2           |          |         |
 +-----------------+-----------------+----------+---------+
 
 For `optional libraries <https://dev.pandas.io/docs/install.html#dependencies>`_ the general recommendation is to use the latest version.
@@ -195,7 +205,7 @@ Optional libraries below the lowest tested version may still work, but are not c
 +-----------------+-----------------+---------+
 | s3fs            | 0.3.0           |         |
 +-----------------+-----------------+---------+
-| scipy           | 0.19.0          |         |
+| scipy           | 1.2.0           |    X    |
 +-----------------+-----------------+---------+
 | sqlalchemy      | 1.1.4           |         |
 +-----------------+-----------------+---------+
diff --git a/environment.yml b/environment.yml
index 8893302b4c9b2..bc7c715104ce5 100644
--- a/environment.yml
+++ b/environment.yml
@@ -75,7 +75,7 @@ dependencies:
   - jinja2  # pandas.Styler
   - matplotlib>=2.2.2  # pandas.plotting, Series.plot, DataFrame.plot
   - numexpr>=2.6.8
-  - scipy>=1.1
+  - scipy>=1.2
   - numba>=0.46.0
 
   # optional for io
diff --git a/pandas/__init__.py b/pandas/__init__.py
index 2b9a461e0e95d..d6584bf4f1c4f 100644
--- a/pandas/__init__.py
+++ b/pandas/__init__.py
@@ -20,8 +20,6 @@
 
 # numpy compat
 from pandas.compat.numpy import (
-    _np_version_under1p14,
-    _np_version_under1p15,
     _np_version_under1p16,
     _np_version_under1p17,
     _np_version_under1p18,
diff --git a/pandas/compat/_optional.py b/pandas/compat/_optional.py
index 7e253a52a9c00..c5fd294699c45 100644
--- a/pandas/compat/_optional.py
+++ b/pandas/compat/_optional.py
@@ -21,7 +21,7 @@
     "pytest": "5.0.1",
     "pyxlsb": "1.0.6",
     "s3fs": "0.3.0",
-    "scipy": "0.19.0",
+    "scipy": "1.2.0",
     "sqlalchemy": "1.1.4",
     "tables": "3.4.3",
     "tabulate": "0.8.3",
diff --git a/pandas/compat/numpy/__init__.py b/pandas/compat/numpy/__init__.py
index 6c9ac5944e6a1..a8f49d91f040e 100644
--- a/pandas/compat/numpy/__init__.py
+++ b/pandas/compat/numpy/__init__.py
@@ -8,19 +8,17 @@
 # numpy versioning
 _np_version = np.__version__
 _nlv = LooseVersion(_np_version)
-_np_version_under1p14 = _nlv < LooseVersion("1.14")
-_np_version_under1p15 = _nlv < LooseVersion("1.15")
 _np_version_under1p16 = _nlv < LooseVersion("1.16")
 _np_version_under1p17 = _nlv < LooseVersion("1.17")
 _np_version_under1p18 = _nlv < LooseVersion("1.18")
 _is_numpy_dev = ".dev" in str(_nlv)
 
 
-if _nlv < "1.13.3":
+if _nlv < "1.15.4":
     raise ImportError(
-        "this version of pandas is incompatible with numpy < 1.13.3\n"
+        "this version of pandas is incompatible with numpy < 1.15.4\n"
         f"your numpy version is {_np_version}.\n"
-        "Please upgrade numpy to >= 1.13.3 to use this pandas version"
+        "Please upgrade numpy to >= 1.15.4 to use this pandas version"
     )
 
 
@@ -65,8 +63,6 @@ def np_array_datetime64_compat(arr, *args, **kwargs):
 __all__ = [
     "np",
     "_np_version",
-    "_np_version_under1p14",
-    "_np_version_under1p15",
     "_np_version_under1p16",
     "_np_version_under1p17",
     "_is_numpy_dev",
diff --git a/pandas/tests/api/test_api.py b/pandas/tests/api/test_api.py
index 5aab5b814bae7..ecd20796b6f21 100644
--- a/pandas/tests/api/test_api.py
+++ b/pandas/tests/api/test_api.py
@@ -193,8 +193,6 @@ class TestPDApi(Base):
         "_hashtable",
         "_lib",
         "_libs",
-        "_np_version_under1p14",
-        "_np_version_under1p15",
         "_np_version_under1p16",
         "_np_version_under1p17",
         "_np_version_under1p18",
diff --git a/pandas/tests/dtypes/cast/test_promote.py b/pandas/tests/dtypes/cast/test_promote.py
index 69f8f46356a4d..74a11c9f33195 100644
--- a/pandas/tests/dtypes/cast/test_promote.py
+++ b/pandas/tests/dtypes/cast/test_promote.py
@@ -98,14 +98,13 @@ def _assert_match(result_fill_value, expected_fill_value):
     # GH#23982/25425 require the same type in addition to equality/NA-ness
     res_type = type(result_fill_value)
     ex_type = type(expected_fill_value)
-    if res_type.__name__ == "uint64":
-        # No idea why, but these (sometimes) do not compare as equal
-        assert ex_type.__name__ == "uint64"
-    elif res_type.__name__ == "ulonglong":
-        # On some builds we get this instead of np.uint64
-        # Note: cant check res_type.dtype.itemsize directly on numpy 1.18
-        assert res_type(0).itemsize == 8
-        assert ex_type == res_type or ex_type == np.uint64
+
+    if hasattr(result_fill_value, "dtype"):
+        # Compare types in a way that is robust to platform-specific
+        #  idiosyncracies where e.g. sometimes we get "ulonglong" as an alias
+        #  for "uint64" or "intc" as an alias for "int32"
+        assert result_fill_value.dtype.kind == expected_fill_value.dtype.kind
+        assert result_fill_value.dtype.itemsize == expected_fill_value.dtype.itemsize
     else:
         # On some builds, type comparison fails, e.g. np.int32 != np.int32
         assert res_type == ex_type or res_type.__name__ == ex_type.__name__
diff --git a/pandas/tests/extension/test_boolean.py b/pandas/tests/extension/test_boolean.py
index 50b72698629bb..04dedac3e8b9b 100644
--- a/pandas/tests/extension/test_boolean.py
+++ b/pandas/tests/extension/test_boolean.py
@@ -16,8 +16,6 @@
 import numpy as np
 import pytest
 
-from pandas.compat.numpy import _np_version_under1p14
-
 import pandas as pd
 import pandas._testing as tm
 from pandas.core.arrays.boolean import BooleanDtype
@@ -111,9 +109,6 @@ def check_opname(self, s, op_name, other, exc=None):
     def _check_op(self, s, op, other, op_name, exc=NotImplementedError):
         if exc is None:
             if op_name in self.implements:
-                # subtraction for bools raises TypeError (but not yet in 1.13)
-                if _np_version_under1p14:
-                    pytest.skip("__sub__ does not yet raise in numpy 1.13")
                 msg = r"numpy boolean subtract"
                 with pytest.raises(TypeError, match=msg):
                     op(s, other)
diff --git a/pandas/tests/frame/methods/test_astype.py b/pandas/tests/frame/methods/test_astype.py
index dc779562b662d..b06c3d72a2c77 100644
--- a/pandas/tests/frame/methods/test_astype.py
+++ b/pandas/tests/frame/methods/test_astype.py
@@ -14,7 +14,6 @@
     Timedelta,
     Timestamp,
     UInt64Index,
-    _np_version_under1p14,
     concat,
     date_range,
     option_context,
@@ -169,9 +168,7 @@ def test_astype_str_float(self):
         tm.assert_frame_equal(result, expected)
         result = DataFrame([1.12345678901234567890]).astype(str)
 
-        # < 1.14 truncates
-        # >= 1.14 preserves the full repr
-        val = "1.12345678901" if _np_version_under1p14 else "1.1234567890123457"
+        val = "1.1234567890123457"
         expected = DataFrame([val])
         tm.assert_frame_equal(result, expected)
 
diff --git a/pyproject.toml b/pyproject.toml
index 696785599d7da..efeb24edbdeb1 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -5,8 +5,8 @@ requires = [
     "setuptools",
     "wheel",
     "Cython>=0.29.16",  # Note: sync with setup.py
-    "numpy==1.13.3; python_version=='3.6' and platform_system!='AIX'",
-    "numpy==1.14.5; python_version>='3.7' and platform_system!='AIX'",
+    "numpy==1.15.4; python_version=='3.6' and platform_system!='AIX'",
+    "numpy==1.15.4; python_version>='3.7' and platform_system!='AIX'",
     "numpy==1.16.0; python_version=='3.6' and platform_system=='AIX'",
     "numpy==1.16.0; python_version>='3.7' and platform_system=='AIX'",
 ]
diff --git a/requirements-dev.txt b/requirements-dev.txt
index 8a954fabd2d8d..5f5b5d27a03a7 100644
--- a/requirements-dev.txt
+++ b/requirements-dev.txt
@@ -50,7 +50,7 @@ ipython>=7.11.1
 jinja2
 matplotlib>=2.2.2
 numexpr>=2.6.8
-scipy>=1.1
+scipy>=1.2
 numba>=0.46.0
 beautifulsoup4>=4.6.0
 html5lib
diff --git a/setup.py b/setup.py
index a2e01e08e8de2..58f3fb5706ad1 100755
--- a/setup.py
+++ b/setup.py
@@ -33,7 +33,7 @@ def is_platform_mac():
     return sys.platform == "darwin"
 
 
-min_numpy_ver = "1.13.3"
+min_numpy_ver = "1.15.4"
 min_cython_ver = "0.29.16"  # note: sync with pyproject.toml
 
 try: