diff --git a/.circleci/config.yml b/.circleci/config.yml
index 3a1bc848942d3..e1e410c440314 100644
--- a/.circleci/config.yml
+++ b/.circleci/config.yml
@@ -65,6 +65,21 @@ jobs:
           path: ~/log.txt
           destination: log.txt
 
+  pypy3:
+    docker:
+      - image: pypy:3-6.0.0
+    steps:
+      - restore_cache:
+          keys:
+            - pypy3-ccache-{{ .Branch }}
+            - pypy3-ccache
+      - checkout
+      - run: ./build_tools/circle/build_test_pypy.sh
+      - save_cache:
+          key: pypy3-ccache-{{ .Branch }}-{{ .BuildNum }}
+          paths:
+            - ~/.ccache
+            - ~/.cache/pip
 
   deploy:
     docker:
@@ -89,6 +104,21 @@ workflows:
     jobs:
       - python3
       - python2
+      - pypy3:
+          filters:
+            branches:
+              only:
+                - 0.20.X
       - deploy:
           requires:
             - python3
+  pypy:
+    triggers:
+      - schedule:
+          cron: "0 0 * * *"
+          filters:
+            branches:
+              only:
+                - master
+    jobs:
+      - pypy3
diff --git a/build_tools/circle/build_test_pypy.sh b/build_tools/circle/build_test_pypy.sh
index 18fa361821d14..922bbac8e23a6 100755
--- a/build_tools/circle/build_test_pypy.sh
+++ b/build_tools/circle/build_test_pypy.sh
@@ -18,13 +18,16 @@ source pypy-env/bin/activate
 python --version
 which python
 
-pip install --extra-index https://antocuni.github.io/pypy-wheels/ubuntu numpy==1.14.4 Cython pytest
+pip install --extra-index https://antocuni.github.io/pypy-wheels/ubuntu numpy Cython pytest
 pip install "scipy>=1.1.0" sphinx numpydoc docutils
 
 ccache -M 512M
 export CCACHE_COMPRESS=1
 export PATH=/usr/lib/ccache:$PATH
+export LOKY_MAX_CPU_COUNT="2"
 
-pip install -e .
+pip install -vv -e . 
 
-make test
+python -m pytest sklearn/
+python -m pytest doc/sphinxext/
+python -m pytest $(find doc -name '*.rst' | sort)
diff --git a/conftest.py b/conftest.py
index f175661165b2d..82c4b17faeef0 100644
--- a/conftest.py
+++ b/conftest.py
@@ -32,7 +32,9 @@ def pytest_collection_modifyitems(config, items):
         skip_marker = pytest.mark.skip(
             reason='FeatureHasher is not compatible with PyPy')
         for item in items:
-            if item.name == 'sklearn.feature_extraction.hashing.FeatureHasher':
+            if item.name in (
+                    'sklearn.feature_extraction.hashing.FeatureHasher',
+                    'sklearn.feature_extraction.text.HashingVectorizer'):
                 item.add_marker(skip_marker)
 
     # Skip tests which require internet if the flag is provided
diff --git a/sklearn/feature_extraction/tests/test_text.py b/sklearn/feature_extraction/tests/test_text.py
index b9431bc5439cb..d6b1b2b64b4c0 100644
--- a/sklearn/feature_extraction/tests/test_text.py
+++ b/sklearn/feature_extraction/tests/test_text.py
@@ -1108,6 +1108,8 @@ def test_vectorizers_invalid_ngram_range(vec):
     message = ("Invalid value for ngram_range=%s "
                "lower boundary larger than the upper boundary."
                % str(invalid_range))
+    if isinstance(vec, HashingVectorizer):
+        pytest.xfail(reason='HashingVectorizer not supported on PyPy')
 
     assert_raise_message(
         ValueError, message, vec.fit, ["good news everyone"])
@@ -1119,6 +1121,7 @@ def test_vectorizers_invalid_ngram_range(vec):
             ValueError, message, vec.transform, ["good news everyone"])
 
 
+@fails_if_pypy
 def test_vectorizer_stop_words_inconsistent():
     if PY2:
         lstr = "[u'and', u'll', u've']"
diff --git a/sklearn/tests/test_docstring_parameters.py b/sklearn/tests/test_docstring_parameters.py
index 648de6b6e6ca5..b4a831e571c4a 100644
--- a/sklearn/tests/test_docstring_parameters.py
+++ b/sklearn/tests/test_docstring_parameters.py
@@ -19,6 +19,8 @@
 from sklearn.utils.testing import ignore_warnings
 from sklearn.utils.deprecation import _is_deprecated
 
+import pytest
+
 PUBLIC_MODULES = set([pckg[1] for pckg in walk_packages(prefix='sklearn.',
                                                         path=sklearn.__path__)
                       if not ("._" in pckg[1] or ".tests." in pckg[1])])
@@ -45,7 +47,8 @@
 
 # numpydoc 0.8.0's docscrape tool raises because of collections.abc under
 # Python 3.7
-@ignore_warnings(category=DeprecationWarning)
+@pytest.mark.filterwarnings('ignore::DeprecationWarning')
+@pytest.mark.skipif(IS_PYPY, reason='test segfaults on PyPy')
 def test_docstring_parameters():
     # Test module docstring formatting