diff --git a/.travis.yml b/.travis.yml
index f43f4a1d16ff8..f16b19814874e 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -46,7 +46,7 @@ matrix:
         # Enabling Deprecations when running tests
         # PANDAS_TESTING_MODE="deprecate" causes DeprecationWarning messages to be displayed in the logs
         # See pandas/_testing.py for more details.
-        - JOB="3.6, coverage" ENV_FILE="ci/deps/travis-36-cov.yaml" PATTERN="((not slow and not network and not clipboard) or (single and db))" PANDAS_TESTING_MODE="deprecate" COVERAGE=true SQL="1"
+        - JOB="3.7, coverage" ENV_FILE="ci/deps/travis-37-cov.yaml" PATTERN="((not slow and not network and not clipboard) or (single and db))" PANDAS_TESTING_MODE="deprecate" COVERAGE=true SQL="1"
       services:
         - mysql
         - postgresql
diff --git a/ci/deps/travis-36-cov.yaml b/ci/deps/travis-37-cov.yaml
similarity index 79%
rename from ci/deps/travis-36-cov.yaml
rename to ci/deps/travis-37-cov.yaml
index 8c8db106af05c..c89b42ef06a2e 100644
--- a/ci/deps/travis-36-cov.yaml
+++ b/ci/deps/travis-37-cov.yaml
@@ -1,9 +1,8 @@
 name: pandas-dev
 channels:
-  - defaults
   - conda-forge
 dependencies:
-  - python=3.6.*
+  - python=3.7.*
 
   # tools
   - cython>=0.29.21
@@ -22,18 +21,21 @@ dependencies:
   - geopandas
   - html5lib
   - matplotlib
-  - moto
+  - moto>=1.3.14
+  - flask
   - nomkl
   - numexpr
-  - numpy=1.15.*
+  - numpy=1.16.*
   - odfpy
   - openpyxl
   - pandas-gbq
+  - google-cloud-bigquery>=1.27.2 # GH 36436
   - psycopg2
-  - pyarrow>=0.13.0
-  - pymysql
+  - pyarrow>=0.15.0
+  - pymysql<0.10.0 # temporary pin, GH 36465
   - pytables
   - python-snappy
+  - python-dateutil
   - pytz
   - s3fs>=0.4.0
   - scikit-learn
@@ -49,5 +51,4 @@ dependencies:
     - brotlipy
     - coverage
     - pandas-datareader
-    - python-dateutil
     - pyxlsb
diff --git a/pandas/tests/groupby/test_categorical.py b/pandas/tests/groupby/test_categorical.py
index 0d447a70b540d..eb3847e9ac19f 100644
--- a/pandas/tests/groupby/test_categorical.py
+++ b/pandas/tests/groupby/test_categorical.py
@@ -3,8 +3,6 @@
 import numpy as np
 import pytest
 
-from pandas.compat import PY37, is_platform_windows
-
 import pandas as pd
 from pandas import (
     Categorical,
@@ -13,7 +11,6 @@
     Index,
     MultiIndex,
     Series,
-    _np_version_under1p17,
     qcut,
 )
 import pandas._testing as tm
@@ -244,12 +241,6 @@ def test_level_get_group(observed):
     tm.assert_frame_equal(result, expected)
 
 
-# GH#21636 flaky on py37; may be related to older numpy, see discussion
-#  https://github.com/MacPython/pandas-wheels/pull/64
-@pytest.mark.xfail(
-    PY37 and _np_version_under1p17 and not is_platform_windows(),
-    reason="Flaky, GH-27902",
-)
 @pytest.mark.parametrize("ordered", [True, False])
 def test_apply(ordered):
     # GH 10138