diff --git a/.appveyor.yml b/.appveyor.yml.back
similarity index 100%
rename from .appveyor.yml
rename to .appveyor.yml.back
diff --git a/.travis.yml b/.travis.yml.back
similarity index 97%
rename from .travis.yml
rename to .travis.yml.back
index 9fbe9ec5..51a07588 100644
--- a/.travis.yml
+++ b/.travis.yml.back
@@ -135,6 +135,6 @@ after_success:
   - pip install wheelhouse-uploader twine
   - python -m twine check ${TRAVIS_BUILD_DIR}/wheelhouse/*
   - python -m wheelhouse_uploader upload --local-folder
-        ${TRAVIS_BUILD_DIR}/wheelhouse/
-        $UPLOAD_ARGS
-        $CONTAINER
+    ${TRAVIS_BUILD_DIR}/wheelhouse/
+    $UPLOAD_ARGS
+    $CONTAINER
diff --git a/README.rst b/README.rst
index cd04d69c..3fce86c1 100644
--- a/README.rst
+++ b/README.rst
@@ -1,7 +1,4 @@
-.. image:: https://travis-ci.org/MacPython/scikit-learn-wheels.svg?branch=master
-    :target: https://travis-ci.org/MacPython/scikit-learn-wheels
-.. image:: https://ci.appveyor.com/api/projects/status/0vgnsltgf2ghhbr2/branch/master?svg=true
-    :target: https://ci.appveyor.com/project/sklearn-wheels/scikit-learn-wheels
+TODO: add Azure Pipelines badge here
 
 ##########################
 Scikit-learn wheel builder
@@ -9,15 +6,17 @@ Scikit-learn wheel builder
 
 Repository to build scikit-learn wheels.
 
-Edit `appveyor.yml` and `.travis.yml` to change the `BUILD_COMMIT` environment
-variable to set the name of the git tag to build, commit and push (to master).
+Edit `azure/windows.yml` and `azure/posix.yml` to change the `BUILD_COMMIT`
+environment variable to set the name of the git tag to build, commit and push
+(to master).
 
-Travis and appveyor should automatically build and test that version on
-Windows, Linux and OSX for various versions of Python (both 32 bit and 64 bit).
+Azure Pipelines should automatically build and test that version on Windows,
+Linux and OSX for various versions of Python (both 32 bit and 64 bit).
 
 If the tests pass, the resulting wheels should show up on:
 
-  http://wheels.scipy.org
+  - https://anaconda.org/scikit-learn-wheels-staging for release wheels staging;
+  - https://anaconda.org/scipy-wheels-nightly for nightly builds.
 
 The following tool can be useful to download all the wheels for a specific
 release:
@@ -25,4 +24,4 @@ release:
   https://github.com/ogrisel/wheelhouse-uploader
 
 and then use `twine` to publish all the wheels along with the locally built
-source tarball of the release all at once to PyPI. 
+source tarball of the release all at once to PyPI.
diff --git a/azure-pipelines.yml b/azure-pipelines.yml
new file mode 100644
index 00000000..f113b606
--- /dev/null
+++ b/azure-pipelines.yml
@@ -0,0 +1,88 @@
+schedules:
+- cron: "27 3 */1 * *"
+  # 3:27am UTC everyday
+  displayName: Nighthly build
+  branches:
+    include:
+    - master
+  always: true
+
+jobs:
+  - template: azure/windows.yml
+    parameters:
+      name: windows
+      vmImage: vs2017-win2016
+      matrix:
+        py_3.6_32:
+          PYTHON_VERSION: "3.6.x"
+          PYTHON_ARCH: "x86"
+          NP_BUILD_DEP: "1.12.1"
+        py_3.6_64:
+          PYTHON_VERSION: "3.6.x"
+          NP_BUILD_DEP: "1.12.1"
+        py_3.7_32:
+          PYTHON_VERSION: "3.7.x"
+          PYTHON_ARCH: "x86"
+          NP_BUILD_DEP: "1.14.5"
+          NIGHTLY_BUILD: "true"
+        py_3.7_64:
+          PYTHON_VERSION: "3.7.x"
+          NP_BUILD_DEP: "1.14.5"
+          NIGHTLY_BUILD: "true"
+        py_3.8_32:
+          PYTHON_VERSION: "3.8.x"
+          PYTHON_ARCH: "x86"
+          NP_BUILD_DEP: "1.17.3"
+          SCIPY_BUILD_DEP: "1.4.1"
+          NIGHTLY_BUILD: "true"
+        py_3.8_64:
+          PYTHON_VERSION: "3.8.x"
+          NP_BUILD_DEP: "1.17.3"
+          SCIPY_BUILD_DEP: "1.4.1"
+          NIGHTLY_BUILD: "true"
+
+  - template: azure/posix.yml
+    parameters:
+      name: linux
+      vmImage: ubuntu-16.04
+      matrix:
+        py_3.6_32:
+          MB_PYTHON_VERSION: "3.6"
+          PLAT: "i686"
+        py_3.6_64:
+          MB_PYTHON_VERSION: "3.6"
+        py_3.7_32:
+          MB_PYTHON_VERSION: "3.7"
+          PLAT: "i686"
+          NP_BUILD_DEP: "numpy==1.14.5"
+          NIGHTLY_BUILD: "true"
+        py_3.7_64:
+          MB_PYTHON_VERSION: "3.7"
+          NP_BUILD_DEP: "numpy==1.14.5"
+          NIGHTLY_BUILD: "true"
+        py_3.8_32:
+          MB_PYTHON_VERSION: "3.8"
+          PLAT: "i686"
+          NP_BUILD_DEP: "numpy==1.17.3"
+          NIGHTLY_BUILD: "true"
+        py_3.8_64:
+          MB_PYTHON_VERSION: "3.8"
+          NP_BUILD_DEP: "numpy==1.17.3"
+          NIGHTLY_BUILD: "true"
+
+  - template: azure/posix.yml
+    parameters:
+      name: macOS
+      vmImage: xcode9-macos10.13
+      matrix:
+        py_3.6_64:
+          MB_PYTHON_VERSION: "3.6"
+          NP_BUILD_DEP: "numpy==1.13.3"
+        py_3.7_64:
+          MB_PYTHON_VERSION: "3.7"
+          NP_BUILD_DEP: "numpy==1.14.5"
+          NIGHTLY_BUILD: "true"
+        py_3.8_64:
+          MB_PYTHON_VERSION: "3.8"
+          NP_BUILD_DEP: "numpy==1.17.3"
+          NIGHTLY_BUILD: "true"
diff --git a/azure/posix.yml b/azure/posix.yml
new file mode 100644
index 00000000..6e28200c
--- /dev/null
+++ b/azure/posix.yml
@@ -0,0 +1,141 @@
+parameters:
+  name: ""
+  vmImage: ""
+  matrix: []
+
+jobs:
+  - job: ${{ parameters.name }}
+    pool:
+      vmImage: ${{ parameters.vmImage }}
+    variables:
+      REPO_DIR: "scikit-learn"
+      BUILD_COMMIT: "0.22.1"
+      PLAT: "x86_64"
+      NP_BUILD_DEP: "numpy==1.11.0"
+      CYTHON_BUILD_DEP: "cython==0.29.14"
+      SCIPY_BUILD_DEP: "scipy"
+      JOBLIB_BUILD_DEP: "joblib==0.11"
+      NIGHTLY_BUILD_COMMIT: "master"
+      NIGHTLY_BUILD: "false"
+      TEST_DEPENDS: "pytest"
+      JUNITXML: "test-data.xml"
+      TEST_DIR: "tmp_for_test"
+    strategy:
+      matrix:
+        ${{ insert }}: ${{ parameters.matrix }}
+
+    steps:
+      - checkout: self
+        submodules: true
+
+      - task: UsePythonVersion@0
+        inputs:
+          versionSpec: $(MB_PYTHON_VERSION)
+        displayName: Set python version
+
+      - bash: |
+          set -e
+
+          SKIP_BUILD="false"
+          if [ "$BUILD_REASON" == "Schedule" ]; then
+            BUILD_COMMIT=$NIGHTLY_BUILD_COMMIT
+            if [ "$NIGHTLY_BUILD" != "true" ]; then
+              SKIP_BUILD="true"
+            fi
+          fi
+          echo "Building scikit-learn@$BUILD_COMMIT"
+          echo "##vso[task.setvariable variable=BUILD_COMMIT]$BUILD_COMMIT"
+          echo "##vso[task.setvariable variable=SKIP_BUILD]$SKIP_BUILD"
+
+          # Platform variables used in multibuild scripts
+          if [ `uname` == 'Darwin' ]; then
+            echo "##vso[task.setvariable variable=TRAVIS_OS_NAME]osx"
+            echo "##vso[task.setvariable variable=MACOSX_DEPLOYMENT_TARGET]10.9"
+          else
+            echo "##vso[task.setvariable variable=TRAVIS_OS_NAME]linux"
+          fi
+
+          # Store original Python path to be able to create test_venv pointing
+          # to same Python version.
+          PYTHON_EXE=`which python`
+          echo "##vso[task.setvariable variable=PYTHON_EXE]$PYTHON_EXE"
+        displayName: Define build env variables
+
+      - bash: |
+          set -e
+          pip install virtualenv
+          BUILD_DEPENDS="$NP_BUILD_DEP $CYTHON_BUILD_DEP $SCIPY_BUILD_DEP"
+
+          source multibuild/common_utils.sh
+          source multibuild/travis_steps.sh
+          source extra_functions.sh
+
+          # Setup build dependencies
+          before_install
+
+          # OpenMP is not present on macOS by default
+          setup_compiler
+          clean_code $REPO_DIR $BUILD_COMMIT
+          build_wheel $REPO_DIR $PLAT
+          teardown_compiler
+        displayName: Build wheel
+        condition: eq(variables['SKIP_BUILD'], 'false')
+
+      - bash: |
+          set -xe
+          source multibuild/common_utils.sh
+          source multibuild/travis_steps.sh
+          source extra_functions.sh
+          setup_test_venv
+          install_run $PLAT
+          teardown_test_venv
+        displayName: Install wheel and test
+        condition: eq(variables['SKIP_BUILD'], 'false')
+
+      - task: PublishTestResults@2
+        inputs:
+          testResultsFiles: '$(TEST_DIR)/$(JUNITXML)'
+          testRunTitle: ${{ format('{0}-$(Agent.JobName)', parameters.name) }}
+        displayName: 'Publish Test Results'
+        condition: eq(variables['SKIP_BUILD'], 'false')
+
+      - bash: |
+          echo "##vso[task.prependpath]$CONDA/bin"
+          sudo chown -R $USER $CONDA
+        displayName: Add conda to PATH
+        condition: and(succeeded(), eq(variables['SKIP_BUILD'], 'false'), ne(variables['Build.Reason'], 'PullRequest'))
+
+      - bash: conda install -q -y anaconda-client
+        displayName: Install anaconda-client
+        condition: and(succeeded(), eq(variables['SKIP_BUILD'], 'false'), ne(variables['Build.Reason'], 'PullRequest'))
+
+      - bash: |
+          set -e
+          if [ "$BUILD_REASON" == "Schedule" ]; then
+            ANACONDA_ORG="scipy-wheels-nightly"
+            TOKEN="$SCIKIT_LEARN_NIGHTLY_UPLOAD_TOKEN"
+          else
+            ANACONDA_ORG="scikit-learn-wheels-staging"
+            TOKEN="$SCIKIT_LEARN_STAGING_UPLOAD_TOKEN"
+          fi
+          if [ "$TOKEN" == "" ]; then
+            echo "##[warning] Could not find anaconda.org upload token in secret variables"
+          fi
+          echo "##vso[task.setvariable variable=TOKEN]$TOKEN"
+          echo "##vso[task.setvariable variable=ANACONDA_ORG]$ANACONDA_ORG"
+        displayName: Retrieve secret upload token
+        condition: and(succeeded(), eq(variables['SKIP_BUILD'], 'false'), ne(variables['Build.Reason'], 'PullRequest'))
+        env:
+          # Secret variables need to mapped to env variables explicitly:
+          SCIKIT_LEARN_NIGHTLY_UPLOAD_TOKEN: $(SCIKIT_LEARN_NIGHTLY_UPLOAD_TOKEN)
+          SCIKIT_LEARN_STAGING_UPLOAD_TOKEN: $(SCIKIT_LEARN_STAGING_UPLOAD_TOKEN)
+
+      - bash: |
+          set -e
+          # The --force option forces a replacement if the remote file already
+          # exists.
+          ls wheelhouse/*.whl
+          anaconda -t $TOKEN upload --force -u $ANACONDA_ORG wheelhouse/*.whl
+          echo "PyPI-style index: https://pypi.anaconda.org/$ANACONDA_ORG/simple"
+        displayName: Upload to anaconda.org (only if secret token is retrieved)
+        condition: ne(variables['TOKEN'], '')
diff --git a/azure/windows.yml b/azure/windows.yml
new file mode 100644
index 00000000..50b85e78
--- /dev/null
+++ b/azure/windows.yml
@@ -0,0 +1,148 @@
+parameters:
+  name: ""
+  vmImage: ""
+  matrix: []
+
+jobs:
+  - job: ${{ parameters.name }}
+    pool:
+      vmImage: ${{ parameters.vmImage }}
+    variables:
+      BUILD_COMMIT: "0.22.1"
+      SKLEARN_SKIP_NETWORK_TESTS: "1"
+      NP_BUILD_DEP: "1.11.0"
+      CYTHON_BUILD_DEP: "0.29.14"
+      SCIPY_BUILD_DEP: "1.1.0"
+      NIGHTLY_BUILD_COMMIT: "master"
+      NIGHTLY_BUILD: "false"
+      PYTHON_ARCH: "x64"
+      TEST_DEPENDS: "pytest"
+      JUNITXML: "test-data.xml"
+      TEST_DIR: '$(Agent.WorkFolder)/tmp_for_test'
+    strategy:
+      matrix:
+        ${{ insert }}: ${{ parameters.matrix }}
+    steps:
+      - checkout: self
+        submodules: true
+
+      - task: UsePythonVersion@0
+        inputs:
+          versionSpec: $(PYTHON_VERSION)
+          architecture: $(PYTHON_ARCH)
+        displayName: Set python version
+
+      - bash: |
+          set -e
+
+          echo PYTHON $PYTHON_VERSION $PYTHON_ARCH
+          echo Build Reason: $BUILD_REASON
+          python --version
+          python -c "import struct; print(struct.calcsize('P') * 8)"
+          pip --version
+        displayName: Check that we have the expected version and architecture for Python
+
+      - bash: |
+          set -e
+
+          SKIP_BUILD="false"
+          if [ "$BUILD_REASON" == "Schedule" ]; then
+            BUILD_COMMIT=$NIGHTLY_BUILD_COMMIT
+            if [ "$NIGHTLY_BUILD" != "true" ]; then
+              SKIP_BUILD="true"
+            fi
+          fi
+          echo "Building scikit-learn@$BUILD_COMMIT"
+          echo "##vso[task.setvariable variable=BUILD_COMMIT]$BUILD_COMMIT"
+          echo "##vso[task.setvariable variable=SKIP_BUILD]$SKIP_BUILD"
+
+          # Store original Python path to be able to create test_venv pointing
+          # to same Python version.
+          PYTHON_EXE=`which python`
+          echo "##vso[task.setvariable variable=PYTHON_EXE]$PYTHON_EXE"
+        displayName: Define build env variables
+
+      - bash: |
+          set -e
+          cd scikit-learn
+          git checkout $BUILD_COMMIT
+          git clean -fxd
+          git reset --hard
+        displayName: Checkout scikit-learn commit
+        condition: eq(variables['SKIP_BUILD'], 'false')
+
+      - bash: |
+          set -e
+
+          pip install --timeout=60 numpy==$NP_BUILD_DEP
+          pip install --timeout=60 pytest wheel joblib scipy==$SCIPY_BUILD_DEP Cython==$CYTHON_BUILD_DEP
+          pip install twine
+
+          pushd scikit-learn
+          python setup.py build
+          python ../appveyor/vendor_vcomp140.py
+          python setup.py bdist_wheel
+          ls dist
+          twine check dist/*
+          popd
+        displayName: Build wheel
+        condition: eq(variables['SKIP_BUILD'], 'false')
+
+      - bash: |
+          set -e
+          source extra_functions.sh
+          setup_test_venv
+          pip install scikit-learn/dist/scikit_learn-*.whl
+          mkdir $TEST_DIR
+          pushd $TEST_DIR
+          pytest -rs -l --junitxml=$JUNITXML --pyargs sklearn
+          popd
+          teardown_test_venv
+        displayName: Install wheel and test
+        condition: eq(variables['SKIP_BUILD'], 'false')
+
+      - task: PublishTestResults@2
+        inputs:
+          testResultsFiles: '$(TEST_DIR)/$(JUNITXML)'
+          testRunTitle: ${{ format('{0}-$(Agent.JobName)', parameters.name) }}
+        displayName: 'Publish Test Results'
+        condition: eq(variables['SKIP_BUILD'], 'false')
+
+      - bash: echo "##vso[task.prependpath]$CONDA/Scripts"
+        displayName: Add conda to PATH
+        condition: and(succeeded(), eq(variables['SKIP_BUILD'], 'false'), ne(variables['Build.Reason'], 'PullRequest'))
+
+      - bash: conda install -q -y anaconda-client
+        displayName: Install anaconda-client
+        condition: and(succeeded(), eq(variables['SKIP_BUILD'], 'false'), ne(variables['Build.Reason'], 'PullRequest'))
+
+      - bash: |
+          set -e
+          if [ "$BUILD_REASON" == "Schedule" ]; then
+            ANACONDA_ORG="scipy-wheels-nightly"
+            TOKEN="$SCIKIT_LEARN_NIGHTLY_UPLOAD_TOKEN"
+          else
+            ANACONDA_ORG="scikit-learn-wheels-staging"
+            TOKEN="$SCIKIT_LEARN_STAGING_UPLOAD_TOKEN"
+          fi
+          if [ "$TOKEN" == "" ]; then
+            echo "##[warning] Could not find anaconda.org upload token in secret variables"
+          fi
+          echo "##vso[task.setvariable variable=TOKEN]$TOKEN"
+          echo "##vso[task.setvariable variable=ANACONDA_ORG]$ANACONDA_ORG"
+        displayName: Retrieve secret upload token
+        condition: and(succeeded(), eq(variables['SKIP_BUILD'], 'false'), ne(variables['Build.Reason'], 'PullRequest'))
+        env:
+          # Secret variables need to mapped to env variables explicitly:
+          SCIKIT_LEARN_NIGHTLY_UPLOAD_TOKEN: $(SCIKIT_LEARN_NIGHTLY_UPLOAD_TOKEN)
+          SCIKIT_LEARN_STAGING_UPLOAD_TOKEN: $(SCIKIT_LEARN_STAGING_UPLOAD_TOKEN)
+
+      - bash: |
+          set -e
+          # The --force option forces a replacement if the remote file already
+          # exists.
+          ls scikit-learn/dist/scikit_learn-*.whl
+          anaconda -t $TOKEN upload --force -u $ANACONDA_ORG scikit-learn/dist/scikit_learn-*.whl
+          echo "PyPI-style index: https://pypi.anaconda.org/$ANACONDA_ORG/simple"
+        displayName: Upload to anaconda.org (only if secret token is retrieved)
+        condition: ne(variables['TOKEN'], '')
diff --git a/config.sh b/config.sh
index ef85678d..a9d40c73 100644
--- a/config.sh
+++ b/config.sh
@@ -7,22 +7,10 @@ function pre_build {
     :
 }
 
+# XXX: test-data.xml is hard-coded because the JUNITXML env variable
+# is not forwarded to the docker container environment.
 function run_tests {
     # Runs tests on installed distribution from an empty directory
     python --version
-    pytest -l --pyargs sklearn
-}
-
- function enable_openmp {
-    # Install OpenMP
-    brew install libomp
-    export CPPFLAGS="$CPPFLAGS -Xpreprocessor -fopenmp"
-    export CFLAGS="$CFLAGS -I/usr/local/opt/libomp/include"
-    export CXXFLAGS="$CXXFLAGS -I/usr/local/opt/libomp/include"
-    export LDFLAGS="$LDFLAGS -L/usr/local/opt/libomp/lib -lomp"
-    export DYLD_LIBRARY_PATH=/usr/local/opt/libomp/lib
-}
-
-function disable_system_openmp {
-    brew uninstall libomp
+    pytest -l --junitxml=test-data.xml --pyargs sklearn
 }
diff --git a/extra_functions.sh b/extra_functions.sh
new file mode 100644
index 00000000..92d20fbf
--- /dev/null
+++ b/extra_functions.sh
@@ -0,0 +1,48 @@
+
+ function setup_compiler {
+    # Install OpenMP support on macOS
+    if [ $(uname) == "Darwin" ]; then
+        brew install libomp
+        export CPPFLAGS="$CPPFLAGS -Xpreprocessor -fopenmp"
+        export CFLAGS="$CFLAGS -I/usr/local/opt/libomp/include"
+        export CXXFLAGS="$CXXFLAGS -I/usr/local/opt/libomp/include"
+        export LDFLAGS="$LDFLAGS -L/usr/local/opt/libomp/lib -lomp"
+        export DYLD_LIBRARY_PATH=/usr/local/opt/libomp/lib
+    fi
+}
+
+function teardown_compiler {
+    if [ $(uname) == "Darwin" ]; then
+        brew uninstall libomp
+    fi
+}
+
+function setup_test_venv {
+    # Create a new empty venv dedicated to testing for non-Linux platforms. On
+    # Linux the tests are run in a Docker container.
+    if [ $(uname) != "Linux" ]; then
+        deactivate || echo ""
+        $PYTHON_EXE -m venv test_venv
+        if [ $(uname) == "Darwin" ]; then
+            source test_venv/bin/activate
+        else
+            source test_venv/Scripts/activate
+        fi
+        # Note: the idiom "python -m pip install ..." is necessary to upgrade
+        # pip itself on Windows. Otherwise one would get a permission error on
+        # pip.exe.
+        python -m pip install --upgrade pip wheel
+        if [ "$TEST_DEPENDS" != "" ]; then
+            pip install $TEST_DEPENDS
+        fi
+    fi
+}
+
+function teardown_test_venv {
+    if [ $(uname) != "Linux" ]; then
+        deactivate || echo ""
+        if [ $(uname) == "Darwin" ]; then
+            source venv/bin/activate
+        fi
+    fi
+}
diff --git a/multibuild b/multibuild
index 68a4af04..6b0ddb52 160000
--- a/multibuild
+++ b/multibuild
@@ -1 +1 @@
-Subproject commit 68a4af043e2adb0d9353d4a0e1f3d871203237aa
+Subproject commit 6b0ddb5281f59d976c8026c082c9d73faf274790