diff --git a/.travis.yml b/.travis.yml
deleted file mode 100644
index 03ba1706..00000000
--- a/.travis.yml
+++ /dev/null
@@ -1,65 +0,0 @@
-language: python
-sudo: false
-cache: pip
-language: python
-env:
-  global:
-    - SKGGM_VERSION=a0ed406586c4364ea3297a658f415e13b5cbdaf8
-matrix:
-  include:
-  - name: "Pytest python 3.6 without skggm"
-    python: "3.6"
-    before_install:
-      - sudo apt-get install liblapack-dev
-      - pip install --upgrade pip pytest
-      - pip install wheel cython numpy scipy codecov pytest-cov scikit-learn
-    script:
-      - pytest test --cov;
-    after_success:
-      - bash <(curl -s https://codecov.io/bash)
-  - name: "Pytest python 3.6 with skggm"
-    python: "3.6"
-    before_install:
-      - sudo apt-get install liblapack-dev
-      - pip install --upgrade pip pytest
-      - pip install wheel cython numpy scipy codecov pytest-cov scikit-learn
-      - pip install git+https://github.com/skggm/skggm.git@${SKGGM_VERSION};
-    script:
-      - pytest test --cov;
-    after_success:
-      - bash <(curl -s https://codecov.io/bash)
-  - name: "Pytest python 3.7 with skggm"
-    python: "3.7"
-    before_install:
-      - sudo apt-get install liblapack-dev
-      - pip install --upgrade pip pytest
-      - pip install wheel cython numpy scipy codecov pytest-cov scikit-learn
-      - pip install git+https://github.com/skggm/skggm.git@${SKGGM_VERSION};
-    script:
-      - pytest test --cov;
-    after_success:
-      - bash <(curl -s https://codecov.io/bash)
-  - name: "Pytest python 3.6 with skggm + scikit-learn 0.20.3"
-    # checks that tests work for the oldest supported scikit-learn version
-    python: "3.6"
-    before_install:
-      - sudo apt-get install liblapack-dev
-      - pip install --upgrade pip pytest
-      - pip install wheel cython numpy scipy codecov pytest-cov
-      - pip install scikit-learn==0.20.3
-      - pip install git+https://github.com/skggm/skggm.git@${SKGGM_VERSION};
-    script:
-      - pytest test --cov;
-    after_success:
-      - bash <(curl -s https://codecov.io/bash)
-  - name: "Syntax checking with flake8"
-    python: "3.7"
-    before_install:
-      - pip install flake8
-    script:
-      - flake8 --extend-ignore=E111,E114 --show-source;
-      # Use this instead to have a syntax check only on the diff:
-      # - source ./build_tools/travis/flake8_diff.sh;
-branches:
-  only:
-  - master
diff --git a/README.rst b/README.rst
index 41181ee8..681e29f6 100644
--- a/README.rst
+++ b/README.rst
@@ -1,4 +1,4 @@
-|Travis-CI Build Status| |License| |PyPI version| |Code coverage|
+|GitHub Actions Build Status| |License| |PyPI version| |Code coverage|
 
 metric-learn: Metric Learning in Python
 =======================================
@@ -67,8 +67,8 @@ Bibtex entry::
 
 .. _sphinx documentation: http://contrib.scikit-learn.org/metric-learn/
 
-.. |Travis-CI Build Status| image:: https://api.travis-ci.org/scikit-learn-contrib/metric-learn.svg?branch=master
-   :target: https://travis-ci.org/scikit-learn-contrib/metric-learn
+.. |GitHub Actions Build Status| image:: https://github.com/scikit-learn-contrib/metric-learn/workflows/CI/badge.svg
+   :target: https://github.com/scikit-learn-contrib/metric-learn/actions?query=event%3Apush+branch%3Amaster
 .. |License| image:: http://img.shields.io/:license-mit-blue.svg?style=flat
    :target: http://badges.mit-license.org
 .. |PyPI version| image:: https://badge.fury.io/py/metric-learn.svg
diff --git a/build_tools/travis/flake8_diff.sh b/build_tools/travis/flake8_diff.sh
deleted file mode 100644
index aea926c8..00000000
--- a/build_tools/travis/flake8_diff.sh
+++ /dev/null
@@ -1,132 +0,0 @@
-# This file is not used yet but we keep it in case we need to check the pep8 difference
-# on the diff (see .travis.yml)
-#
-#!/bin/bash
-# copied-pasted and adapted from http://github.com/sklearn-contrib/imbalanced-learn
-# (more precisely: https://raw.githubusercontent.com/glemaitre/imbalanced-learn
-# /adcb9d8e6210b321dac2c1b06879e5e889d52d77/build_tools/travis/flake8_diff.sh)
-
-# This script is used in Travis to check that PRs do not add obvious
-# flake8 violations. It relies on two things:
-#   - find common ancestor between branch and
-#     scikit-learn/scikit-learn remote
-#   - run flake8 --diff on the diff between the branch and the common
-#     ancestor
-#
-# Additional features:
-#   - the line numbers in Travis match the local branch on the PR
-#     author machine.
-#   - ./build_tools/travis/flake8_diff.sh can be run locally for quick
-#     turn-around
-
-set -e
-# pipefail is necessary to propagate exit codes
-set -o pipefail
-
-PROJECT=scikit-learn-contrib/metric-learn
-PROJECT_URL=https://github.com/$PROJECT.git
-
-# Find the remote with the project name (upstream in most cases)
-REMOTE=$(git remote -v | grep $PROJECT | cut -f1 | head -1 || echo '')
-
-# Add a temporary remote if needed. For example this is necessary when
-# Travis is configured to run in a fork. In this case 'origin' is the
-# fork and not the reference repo we want to diff against.
-if [[ -z "$REMOTE" ]]; then
-    TMP_REMOTE=tmp_reference_upstream
-    REMOTE=$TMP_REMOTE
-    git remote add $REMOTE $PROJECT_URL
-fi
-
-echo "Remotes:"
-echo '--------------------------------------------------------------------------------'
-git remote --verbose
-
-# Travis does the git clone with a limited depth (50 at the time of
-# writing). This may not be enough to find the common ancestor with
-# $REMOTE/master so we unshallow the git checkout
-if [[ -a .git/shallow ]]; then
-    echo -e '\nTrying to unshallow the repo:'
-    echo '--------------------------------------------------------------------------------'
-    git fetch --unshallow
-fi
-
-if [[ "$TRAVIS" == "true" ]]; then
-    if [[ "$TRAVIS_PULL_REQUEST" == "false" ]]
-    then
-        # In main repo, using TRAVIS_COMMIT_RANGE to test the commits
-        # that were pushed into a branch
-        if [[ "$PROJECT" == "$TRAVIS_REPO_SLUG" ]]; then
-            if [[ -z "$TRAVIS_COMMIT_RANGE" ]]; then
-                echo "New branch, no commit range from Travis so passing this test by convention"
-                exit 0
-            fi
-            COMMIT_RANGE=$TRAVIS_COMMIT_RANGE
-        fi
-    else
-        # We want to fetch the code as it is in the PR branch and not
-        # the result of the merge into master. This way line numbers
-        # reported by Travis will match with the local code.
-        LOCAL_BRANCH_REF=travis_pr_$TRAVIS_PULL_REQUEST
-        # In Travis the PR target is always origin
-        git fetch origin pull/$TRAVIS_PULL_REQUEST/head:refs/$LOCAL_BRANCH_REF
-    fi
-fi
-
-# If not using the commit range from Travis we need to find the common
-# ancestor between $LOCAL_BRANCH_REF and $REMOTE/master
-if [[ -z "$COMMIT_RANGE" ]]; then
-    if [[ -z "$LOCAL_BRANCH_REF" ]]; then
-        LOCAL_BRANCH_REF=$(git rev-parse --abbrev-ref HEAD)
-    fi
-    echo -e "\nLast 2 commits in $LOCAL_BRANCH_REF:"
-    echo '--------------------------------------------------------------------------------'
-    git log -2 $LOCAL_BRANCH_REF
-
-    REMOTE_MASTER_REF="$REMOTE/master"
-    # Make sure that $REMOTE_MASTER_REF is a valid reference
-    echo -e "\nFetching $REMOTE_MASTER_REF"
-    echo '--------------------------------------------------------------------------------'
-    git fetch $REMOTE master:refs/remotes/$REMOTE_MASTER_REF
-    LOCAL_BRANCH_SHORT_HASH=$(git rev-parse --short $LOCAL_BRANCH_REF)
-    REMOTE_MASTER_SHORT_HASH=$(git rev-parse --short $REMOTE_MASTER_REF)
-
-    COMMIT=$(git merge-base $LOCAL_BRANCH_REF $REMOTE_MASTER_REF) || \
-        echo "No common ancestor found for $(git show $LOCAL_BRANCH_REF -q) and $(git show $REMOTE_MASTER_REF -q)"
-
-    if [ -z "$COMMIT" ]; then
-        exit 1
-    fi
-
-    COMMIT_SHORT_HASH=$(git rev-parse --short $COMMIT)
-
-    echo -e "\nCommon ancestor between $LOCAL_BRANCH_REF ($LOCAL_BRANCH_SHORT_HASH)"\
-         "and $REMOTE_MASTER_REF ($REMOTE_MASTER_SHORT_HASH) is $COMMIT_SHORT_HASH:"
-    echo '--------------------------------------------------------------------------------'
-    git show --no-patch $COMMIT_SHORT_HASH
-
-    COMMIT_RANGE="$COMMIT_SHORT_HASH..$LOCAL_BRANCH_SHORT_HASH"
-
-    if [[ -n "$TMP_REMOTE" ]]; then
-        git remote remove $TMP_REMOTE
-    fi
-
-else
-    echo "Got the commit range from Travis: $COMMIT_RANGE"
-fi
-
-echo -e '\nRunning flake8 on the diff in the range' "$COMMIT_RANGE" \
-     "($(git rev-list $COMMIT_RANGE | wc -l) commit(s)):"
-echo '--------------------------------------------------------------------------------'
-
-# to not include the context (some lines before and after the modified lines), add the
-# flag --unified=0 (warning: it will not include some errors like for instance adding too
-# much blank lines
-check_files() {
-    git diff $COMMIT_RANGE | flake8 --diff --show-source --extend-ignore=E111,E114
-}
-
-check_files
-
-echo -e "No problem detected by flake8\n"
-