diff --git a/.cirrus.yml b/.cirrus.yml
new file mode 100644
index 0000000000000..f4386a3d7e5a2
--- /dev/null
+++ b/.cirrus.yml
@@ -0,0 +1,171 @@
+env:
+  WIDEMUL: auto
+  BIGNUM: auto
+  STATICPRECOMPUTATION: yes
+  ECMULTGENPRECISION: auto
+  ASM: no
+  BUILD: check
+  WITH_VALGRIND: yes
+  RUN_VALGRIND: no
+  EXTRAFLAGS:
+  HOST:
+  ECDH: no
+  RECOVERY: no
+  SCHNORRSIG: no
+  EXPERIMENTAL: no
+  CTIMETEST: yes
+  BENCH: yes
+  ITERS: 2
+  # We only need the top commit
+  CIRRUS_CLONE_DEPTH: 1
+
+cat_logs_snippet: &CAT_LOGS
+  always:
+    test_logs_script:
+      - cat tests.log || true
+      - cat exhaustive_tests.log || true
+      - cat valgrind_ctime_test.log || true
+      - cat bench.log || true
+  on_failure:
+    debug_output_script:
+      - cat config.log || true
+      - cat test_env.log || true
+      - env
+
+task:
+  name: "x86_64: Linux (Alpine Linux, Nix Shell)"
+  container:
+    dockerfile: ci/linux-nixos.Dockerfile
+    # Reduce number of CPUs to be able to do more builds in parallel.
+    cpu: 1
+    # More than enough for our scripts.
+    memory: 1G
+  matrix: &ENV_MATRIX
+    - env: {WIDEMUL:  int64,  RECOVERY: yes}
+    - env: {WIDEMUL:  int64,                 ECDH: yes, EXPERIMENTAL: yes, SCHNORRSIG: yes}
+    - env: {WIDEMUL: int128}
+    - env: {WIDEMUL: int128,  RECOVERY: yes,            EXPERIMENTAL: yes, SCHNORRSIG: yes}
+    - env: {WIDEMUL: int128,                 ECDH: yes, EXPERIMENTAL: yes, SCHNORRSIG: yes}
+    - env: {WIDEMUL: int128,  ASM: x86_64}
+    - env: {BIGNUM: no}
+    - env: {BIGNUM: no,       RECOVERY: yes,            EXPERIMENTAL: yes, SCHNORRSIG: yes}
+    - env: {BIGNUM: no,       STATICPRECOMPUTATION: no}
+    - env: {BUILD: distcheck, WITH_VALGRIND: no, CTIMETEST: no, BENCH: no}
+    - env: {CPPFLAGS: -DDETERMINISTIC}
+    - env: {CFLAGS: -O0, CTIMETEST: no}
+    - env:
+        CFLAGS:  "-fsanitize=undefined -fno-omit-frame-pointer"
+        LDFLAGS: "-fsanitize=undefined -fno-omit-frame-pointer"
+        UBSAN_OPTIONS: "print_stacktrace=1:halt_on_error=1"
+        BIGNUM: no
+        ASM: x86_64
+        ECDH: yes
+        RECOVERY: yes
+        EXPERIMENTAL: yes
+        SCHNORRSIG: yes
+        CTIMETEST: no
+    - env: { ECMULTGENPRECISION: 2 }
+    - env: { ECMULTGENPRECISION: 8 }
+    - env:
+        RUN_VALGRIND: yes
+        BIGNUM: no
+        ASM: x86_64
+        ECDH: yes
+        RECOVERY: yes
+        EXPERIMENTAL: yes
+        SCHNORRSIG: yes
+        EXTRAFLAGS: "--disable-openssl-tests"
+        BUILD:
+  matrix:
+    - env:
+        CC: gcc
+    - env:
+        CC: clang
+  test_script:
+    - nix-shell ci/shell.nix --run ./ci/cirrus.sh
+  << : *CAT_LOGS
+
+task:
+  name: "i686: Linux (Alpine Linux, Nix Shell)"
+  container:
+    dockerfile: ci/linux-nixos.Dockerfile
+    cpu: 1
+    memory: 1G
+  env:
+    HOST: i686-linux-gnu
+    ECDH: yes
+    RECOVERY: yes
+    EXPERIMENTAL: yes
+    SCHNORRSIG: yes
+  matrix:
+    - env:
+        CC: gcc
+    - env:
+        CC: clang
+  matrix:
+    - env:
+        BIGNUM: gmp
+    - env:
+        BIGNUM: no
+  test_script:
+    - nix-shell ci/shell-i686.nix --run ./ci/cirrus.sh
+  << : *CAT_LOGS
+
+task:
+  name: "x86_64: macOS Catalina"
+  macos_instance:
+    image: catalina-base
+  matrix:
+    << : *ENV_MATRIX
+  matrix:
+    - env:
+        CC: gcc-9
+    - env:
+        CC: clang
+  # Update Command Line Tools
+  # Uncomment this if the Command Line Tools on the CirrusCI macOS image are too old to brew valgrind.
+  # See https://apple.stackexchange.com/a/195963 for the implementation.
+  ## update_clt_script:
+  ##   - system_profiler SPSoftwareDataType
+  ##   - touch /tmp/.com.apple.dt.CommandLineTools.installondemand.in-progress
+  ##   - |-
+  ##     PROD=$(softwareupdate -l | grep "*.*Command Line" | tail -n 1 | awk -F"*" '{print $2}' | sed -e 's/^ *//' | sed 's/Label: //g' | tr -d '\n')
+  ##   # For debugging
+  ##   - softwareupdate -l && echo "PROD: $PROD"
+  ##   - softwareupdate -i "$PROD" --verbose
+  ##   - rm /tmp/.com.apple.dt.CommandLineTools.installondemand.in-progress
+  ##
+  brew_script:
+    # TODO cache the binaries
+    - export HOMEBREW_NO_AUTO_UPDATE=1
+    - export HOMEBREW_NO_INSTALL_CLEANUP=1
+    - brew config
+    - brew tap --shallow LouisBrunner/valgrind
+    - brew install --HEAD LouisBrunner/valgrind/valgrind
+    - brew install automake libtool gmp gcc@9
+  test_script:
+    - ./ci/cirrus.sh
+  << : *CAT_LOGS
+
+task:
+  name: "s390x (big-endian): Linux (Debian QEMU)"
+  container:
+    dockerfile: ci/linux-debian-s390-qemu.Dockerfile
+    cpu: 1
+    memory: 1G
+  env:
+    QEMU_CMD: qemu-s390x
+    HOST: s390x-linux-gnu
+    BUILD:
+    WITH_VALGRIND: no
+    BIGNUM: no
+    ECDH: yes
+    RECOVERY: yes
+    EXPERIMENTAL: yes
+    SCHNORRSIG: yes
+    CTIMETEST: no
+  test_script:
+    # https://sourceware.org/bugzilla/show_bug.cgi?id=27008
+    - rm /etc/ld.so.cache
+    - ./ci/cirrus.sh
+  << : *CAT_LOGS
diff --git a/.travis.yml b/.travis.yml
index 91f1d41a2a38b..0699aa0caccf7 100644
--- a/.travis.yml
+++ b/.travis.yml
@@ -97,7 +97,7 @@ before_script: ./autogen.sh
 script:
   - function keep_alive() { while true; do echo -en "\a"; sleep 60; done }
   - keep_alive &
-  - ./contrib/travis.sh
+  - ./ci/travis.sh
   - kill %keep_alive
 
 after_script:
diff --git a/README.md b/README.md
index e070937235c36..b34102145e04e 100644
--- a/README.md
+++ b/README.md
@@ -2,6 +2,7 @@ libsecp256k1
 ============
 
 [![Build Status](https://travis-ci.org/bitcoin-core/secp256k1.svg?branch=master)](https://travis-ci.org/bitcoin-core/secp256k1)
+[![Build Status](https://api.cirrus-ci.com/github/bitcoin-core/secp256k1.svg?branch=master)](https://cirrus-ci.com/github/bitcoin-core/secp256k1)
 
 Optimized C library for ECDSA signatures and secret/public key operations on curve secp256k1.
 
diff --git a/ci/cirrus.sh b/ci/cirrus.sh
new file mode 100755
index 0000000000000..e10037a468474
--- /dev/null
+++ b/ci/cirrus.sh
@@ -0,0 +1,84 @@
+#!/bin/sh
+
+set -e
+set -x
+
+export LC_ALL=C
+
+env >> test_env.log
+
+$CC -v || true
+valgrind --version || true
+
+./autogen.sh
+
+# Nix doesn't store GNU file in /usr/bin, see https://lists.gnu.org/archive/html/bug-libtool/2015-09/msg00000.html .
+# The -i'' is necessary for macOS portability, see https://stackoverflow.com/a/4247319 .
+sed -i'' -e 's@/usr/bin/file@$(which file)@g' configure
+
+./configure \
+    --enable-experimental="$EXPERIMENTAL" \
+    --with-test-override-wide-multiply="$WIDEMUL" --with-bignum="$BIGNUM" --with-asm="$ASM" \
+    --enable-ecmult-static-precomputation="$STATICPRECOMPUTATION" --with-ecmult-gen-precision="$ECMULTGENPRECISION" \
+    --enable-module-ecdh="$ECDH" --enable-module-recovery="$RECOVERY" \
+    --enable-module-schnorrsig="$SCHNORRSIG" \
+    --with-valgrind="$WITH_VALGRIND" \
+    --host="$HOST" $EXTRAFLAGS
+
+if [ -n "$BUILD" ]
+then
+    make -j2 "$BUILD"
+fi
+
+if [ "$RUN_VALGRIND" = "yes" ]
+then
+    make -j2
+    # the `--error-exitcode` is required to make the test fail if valgrind found errors, otherwise it'll return 0 (https://www.valgrind.org/docs/manual/manual-core.html)
+    valgrind --error-exitcode=42 ./tests 16
+    valgrind --error-exitcode=42 ./exhaustive_tests
+fi
+
+if [ -n "$QEMU_CMD" ]
+then
+    make -j2
+    $QEMU_CMD ./tests 16
+    $QEMU_CMD ./exhaustive_tests
+fi
+
+if [ "$BENCH" = "yes" ]
+then
+    # Using the local `libtool` because on macOS the system's libtool has nothing to do with GNU libtool
+    EXEC='./libtool --mode=execute'
+    if [ -n "$QEMU_CMD" ]
+    then
+       EXEC="$EXEC $QEMU_CMD"
+    fi
+    if [ "$RUN_VALGRIND" = "yes" ]
+    then
+        EXEC="$EXEC valgrind --error-exitcode=42"
+    fi
+    # This limits the iterations in the benchmarks below to ITER iterations.
+    export SECP256K1_BENCH_ITERS="$ITERS"
+    {
+        $EXEC ./bench_ecmult
+        $EXEC ./bench_internal
+        $EXEC ./bench_sign
+        $EXEC ./bench_verify
+    } >> bench.log 2>&1
+    if [ "$RECOVERY" = "yes" ]
+    then
+        $EXEC ./bench_recover >> bench.log 2>&1
+    fi
+    if [ "$ECDH" = "yes" ]
+    then
+        $EXEC ./bench_ecdh >> bench.log 2>&1
+    fi
+    if [ "$SCHNORRSIG" = "yes" ]
+    then
+        $EXEC ./bench_schnorrsig >> bench.log 2>&1
+    fi
+fi
+if [ "$CTIMETEST" = "yes" ]
+then
+    ./libtool --mode=execute valgrind --error-exitcode=42 ./valgrind_ctime_test > valgrind_ctime_test.log 2>&1
+fi
diff --git a/ci/linux-debian-s390-qemu.Dockerfile b/ci/linux-debian-s390-qemu.Dockerfile
new file mode 100644
index 0000000000000..d527be55cb23f
--- /dev/null
+++ b/ci/linux-debian-s390-qemu.Dockerfile
@@ -0,0 +1,6 @@
+FROM debian
+
+RUN dpkg --add-architecture s390x
+RUN apt-get update
+RUN apt-get install --no-install-recommends --no-upgrade -y make automake libtool
+RUN apt-get install --no-install-recommends --no-upgrade -y gcc-s390x-linux-gnu libc6-dev-s390x-cross qemu-user libc6:s390x
diff --git a/ci/linux-nixos.Dockerfile b/ci/linux-nixos.Dockerfile
new file mode 100644
index 0000000000000..0017073c9dc3d
--- /dev/null
+++ b/ci/linux-nixos.Dockerfile
@@ -0,0 +1,12 @@
+FROM nixos/nix
+
+COPY ci/shell.nix /tmp
+COPY ci/shell-i686.nix /tmp
+
+RUN nix-channel --remove nixpkgs
+RUN nix-channel --add https://nixos.org/channels/nixos-20.09 nixpkgs
+RUN nix-channel --update
+
+# Run dummy command "true" in the nix-shell just to get the packages prepared.
+RUN nix-shell /tmp/shell.nix --command true
+RUN nix-shell /tmp/shell-i686.nix --command true
diff --git a/ci/shell-i686.nix b/ci/shell-i686.nix
new file mode 100644
index 0000000000000..6ab4f121bd35a
--- /dev/null
+++ b/ci/shell-i686.nix
@@ -0,0 +1,9 @@
+with (import <nixpkgs> {}).pkgsi686Linux;
+mkShell {
+   buildInputs = [
+       bash file pkgconfig autoconf automake libtool gmp valgrind clang gcc
+   ];
+   shellHook = ''
+       echo Running nix-shell with nixpkgs version: $(nix eval --raw nixpkgs.lib.version)
+   '';
+}
diff --git a/ci/shell.nix b/ci/shell.nix
new file mode 100644
index 0000000000000..2ce852515b4d4
--- /dev/null
+++ b/ci/shell.nix
@@ -0,0 +1,9 @@
+with (import <nixpkgs> {});
+mkShell {
+   buildInputs = [
+       bash file pkgconfig autoconf automake libtool gmp valgrind clang gcc
+   ];
+   shellHook = ''
+       echo Running nix-shell with nixpkgs version: $(nix eval --raw nixpkgs.lib.version)
+   '';
+}
diff --git a/contrib/travis.sh b/ci/travis.sh
similarity index 100%
rename from contrib/travis.sh
rename to ci/travis.sh