diff --git a/tests/compat-in-docker.sh b/tests/compat-in-docker.sh
new file mode 100755
index 0000000..bbb860a
--- /dev/null
+++ b/tests/compat-in-docker.sh
@@ -0,0 +1,52 @@
+#!/bin/bash -eu
+
+# compat-in-docker.sh
+#
+# This file is part of mbed TLS (https://tls.mbed.org)
+#
+# Copyright (c) 2019, ARM Limited, All Rights Reserved
+#
+# Purpose
+# -------
+# This runs compat.sh in a Docker container.
+#
+# Notes for users
+# ---------------
+# If OPENSSL_CMD, GNUTLS_CLI, or GNUTLS_SERV are specified the path must
+# correspond to an executable inside the Docker container. The special
+# values "next" (OpenSSL only) and "legacy" are also allowed as shorthand
+# for the installations inside the container.
+#
+# See also:
+# - scripts/docker_env.sh for general Docker prerequisites and other information.
+# - compat.sh for notes about invocation of that script.
+
+source tests/scripts/docker_env.sh
+
+case "${OPENSSL_CMD:-default}" in
+    "legacy")  export OPENSSL_CMD="/usr/local/openssl-1.0.1j/bin/openssl";;
+    "next")    export OPENSSL_CMD="/usr/local/openssl-1.1.1a/bin/openssl";;
+    *) ;;
+esac
+
+case "${GNUTLS_CLI:-default}" in
+    "legacy")  export GNUTLS_CLI="/usr/local/gnutls-3.3.8/bin/gnutls-cli";;
+    "next")  export GNUTLS_CLI="/usr/local/gnutls-3.6.5/bin/gnutls-cli";;
+    *) ;;
+esac
+
+case "${GNUTLS_SERV:-default}" in
+    "legacy")  export GNUTLS_SERV="/usr/local/gnutls-3.3.8/bin/gnutls-serv";;
+    "next")  export GNUTLS_SERV="/usr/local/gnutls-3.6.5/bin/gnutls-serv";;
+    *) ;;
+esac
+
+run_in_docker \
+    -e M_CLI \
+    -e M_SRV \
+    -e GNUTLS_CLI \
+    -e GNUTLS_SERV \
+    -e OPENSSL_CMD \
+    -e OSSL_NO_DTLS \
+    tests/compat.sh \
+    $@
diff --git a/tests/docker/xenial/Dockerfile b/tests/docker/xenial/Dockerfile
new file mode 100644
index 0000000..4573af9
--- /dev/null
+++ b/tests/docker/xenial/Dockerfile
@@ -0,0 +1,153 @@
+#
+# This file is part of mbed TLS (https://tls.mbed.org)
+#
+# Copyright (c) 2018-2019, ARM Limited, All Rights Reserved
+#
+# Purpose
+#
+# Defines a Docker container suitable to build and run all tests (all.sh),
+# except for those that use a proprietary toolchain.
+
+FROM ubuntu:xenial
+
+ARG MAKEFLAGS_PARALLEL=""
+
+ENV DEBIAN_FRONTEND noninteractive
+
+RUN apt update \
+    && apt -y install software-properties-common \
+    && rm -rf /var/lib/apt/lists
+
+RUN add-apt-repository -y ppa:team-gcc-arm-embedded/ppa
+
+RUN apt-get update \
+    && apt-get -y install \
+    # mbedtls build/test dependencies
+    build-essential \
+    clang \
+    cmake \
+    doxygen \
+    gcc-arm-none-eabi \
+    gcc-mingw-w64-i686 \
+    gcc-multilib \
+    g++-multilib \
+    gdb \
+    git \
+    graphviz \
+    lsof \
+    python \
+    python3-pip \
+    python3 \
+    pylint3 \
+    valgrind \
+    wget \
+    # libnettle build dependencies
+    libgmp-dev \
+    m4 \
+    pkg-config \
+    && rm -rf /var/lib/apt/lists/*
+
+# Build a static, legacy openssl from sources with sslv3 enabled
+# Based on https://gist.github.com/bmaupin/8caca3a1e8c3c5686141 (build-openssl.sh)
+# Note: openssl-1.0.2 and earlier has known build issues with parallel make.
+RUN cd /tmp \
+    && wget https://www.openssl.org/source/old/1.0.1/openssl-1.0.1j.tar.gz -qO- | tar xz \
+    && cd openssl-1.0.1j \
+    && ./config --openssldir=/usr/local/openssl-1.0.1j no-shared \
+    && (make ${MAKEFLAGS_PARALLEL} || make -j 1) \
+    && make install_sw \
+    && rm -rf /tmp/openssl*
+ENV OPENSSL_LEGACY=/usr/local/openssl-1.0.1j/bin/openssl
+
+# Build OPENSSL as 1.0.2g
+RUN cd /tmp \
+    && wget https://www.openssl.org/source/old/1.0.2/openssl-1.0.2g.tar.gz -qO- | tar xz \
+    && cd openssl-1.0.2g \
+    && ./config --openssldir=/usr/local/openssl-1.0.2g no-shared \
+    && (make ${MAKEFLAGS_PARALLEL} || make -j 1) \
+    && make install_sw \
+    && rm -rf /tmp/openssl*
+ENV OPENSSL=/usr/local/openssl-1.0.2g/bin/openssl
+
+# Build a new openssl binary for ARIA/CHACHA20 support
+# Based on https://gist.github.com/bmaupin/8caca3a1e8c3c5686141 (build-openssl.sh)
+RUN cd /tmp \
+    && wget https://www.openssl.org/source/openssl-1.1.1a.tar.gz -qO- | tar xz \
+    && cd openssl-1.1.1a \
+    && ./config --prefix=/usr/local/openssl-1.1.1a -Wl,--enable-new-dtags,-rpath,'${LIBRPATH}' no-shared \
+    && make ${MAKEFLAGS_PARALLEL} \
+    && make install_sw \
+    && rm -rf /tmp/openssl*
+ENV OPENSSL_NEXT=/usr/local/openssl-1.1.1a/bin/openssl
+
+# Build libnettle 2.7.1 (needed by legacy gnutls)
+RUN cd /tmp \
+    && wget https://ftp.gnu.org/gnu/nettle/nettle-2.7.1.tar.gz -qO- | tar xz \
+    && cd nettle-2.7.1 \
+    && ./configure --disable-documentation \
+    && make ${MAKEFLAGS_PARALLEL} \
+    && make install \
+    && /sbin/ldconfig \
+    && rm -rf /tmp/nettle*
+
+# Build legacy gnutls (3.3.8)
+RUN cd /tmp \
+    && wget https://www.gnupg.org/ftp/gcrypt/gnutls/v3.3/gnutls-3.3.8.tar.xz -qO- | tar xJ \
+    && cd gnutls-3.3.8 \
+    && ./configure --prefix=/usr/local/gnutls-3.3.8 --exec_prefix=/usr/local/gnutls-3.3.8 --disable-shared --disable-guile --disable-doc \
+    && make ${MAKEFLAGS_PARALLEL} \
+    && make install \
+    && rm -rf /tmp/gnutls*
+ENV GNUTLS_LEGACY_CLI=/usr/local/gnutls-3.3.8/bin/gnutls-cli
+ENV GNUTLS_LEGACY_SERV=/usr/local/gnutls-3.3.8/bin/gnutls-serv
+
+# Build libnettle 3.1 (needed by gnutls)
+RUN cd /tmp \
+    && wget https://ftp.gnu.org/gnu/nettle/nettle-3.1.tar.gz -qO- | tar xz \
+    && cd nettle-3.1 \
+    && ./configure --disable-documentation \
+    && make ${MAKEFLAGS_PARALLEL} \
+    && make install \
+    && /sbin/ldconfig \
+    && rm -rf /tmp/nettle*
+
+# Build gnutls (3.4.10)
+RUN cd /tmp \
+    && wget https://www.gnupg.org/ftp/gcrypt/gnutls/v3.4/gnutls-3.4.10.tar.xz -qO- | tar xJ \
+    && cd gnutls-3.4.10 \
+    && ./configure --prefix=/usr/local/gnutls-3.4.10 --exec_prefix=/usr/local/gnutls-3.4.10 \
+        --with-included-libtasn1 --without-p11-kit \
+        --disable-shared --disable-guile --disable-doc \
+    && make ${MAKEFLAGS_PARALLEL} \
+    && make install \
+    && rm -rf /tmp/gnutls*
+ENV GNUTLS_CLI=/usr/local/gnutls-3.4.10/bin/gnutls-cli
+ENV GNUTLS_SERV=/usr/local/gnutls-3.4.10/bin/gnutls-serv
+
+# Build libnettle 3.4 (needed by gnutls next)
+RUN cd /tmp \
+    && wget https://ftp.gnu.org/gnu/nettle/nettle-3.4.1.tar.gz -qO- | tar xz \
+    && cd nettle-3.4.1 \
+    && ./configure --disable-documentation \
+    && make ${MAKEFLAGS_PARALLEL} \
+    && make install \
+    && /sbin/ldconfig \
+    && rm -rf /tmp/nettle*
+
+# Build gnutls next (3.6.5)
+RUN cd /tmp \
+    && wget https://www.gnupg.org/ftp/gcrypt/gnutls/v3.6/gnutls-3.6.5.tar.xz -qO- | tar xJ \
+    && cd gnutls-3.6.5 \
+    && ./configure --prefix=/usr/local/gnutls-3.6.5 --exec_prefix=/usr/local/gnutls-3.6.5 \
+        --with-included-libtasn1 --with-included-unistring --without-p11-kit \
+        --disable-shared --disable-guile --disable-doc \
+    && make ${MAKEFLAGS_PARALLEL} \
+    && make install \
+    && rm -rf /tmp/gnutls*
+
+ENV GNUTLS_NEXT_CLI=/usr/local/gnutls-3.6.5/bin/gnutls-cli
+ENV GNUTLS_NEXT_SERV=/usr/local/gnutls-3.6.5/bin/gnutls-serv
+
+RUN pip3 install --no-cache-dir \
+    mbed-host-tests \
+    mock
diff --git a/tests/make-in-docker.sh b/tests/make-in-docker.sh
new file mode 100755
index 0000000..2f8b901
--- /dev/null
+++ b/tests/make-in-docker.sh
@@ -0,0 +1,18 @@
+#!/bin/bash -eu
+
+# make-in-docker.sh
+#
+# This file is part of mbed TLS (https://tls.mbed.org)
+#
+# Copyright (c) 2019, ARM Limited, All Rights Reserved
+#
+# Purpose
+# -------
+# This runs make in a Docker container.
+#
+# See also:
+# - scripts/docker_env.sh for general Docker prerequisites and other information.
+
+source tests/scripts/docker_env.sh
+
+run_in_docker make $@
diff --git a/tests/scripts/all-in-docker.sh b/tests/scripts/all-in-docker.sh
new file mode 100755
index 0000000..3d5dbf2
--- /dev/null
+++ b/tests/scripts/all-in-docker.sh
@@ -0,0 +1,24 @@
+#!/bin/bash -eu
+
+# all-in-docker.sh
+#
+# This file is part of mbed TLS (https://tls.mbed.org)
+#
+# Copyright (c) 2018-2019, ARM Limited, All Rights Reserved
+#
+# Purpose
+# -------
+# This runs all.sh (except for armcc) in a Docker container.
+#
+# Notes for users
+# ---------------
+# See docker_env.sh for prerequisites and other information.
+#
+# See also all.sh for notes about invocation of that script.
+
+source tests/scripts/docker_env.sh
+
+# Run tests that are possible with openly available compilers
+run_in_docker tests/scripts/all.sh \
+    --no-armcc \
+    $@
diff --git a/tests/scripts/basic-in-docker.sh b/tests/scripts/basic-in-docker.sh
new file mode 100755
index 0000000..cfb72f4
--- /dev/null
+++ b/tests/scripts/basic-in-docker.sh
@@ -0,0 +1,37 @@
+#!/bin/bash -eu
+
+# basic-in-docker.sh
+#
+# This file is part of mbed TLS (https://tls.mbed.org)
+#
+# Copyright (c) 2018-2019, ARM Limited, All Rights Reserved
+#
+# Purpose
+# -------
+# This runs a rough equivalent of the travis.yml in a Docker container.
+# The tests are run for both clang and gcc.
+#
+# Notes for users
+# ---------------
+# See docker_env.sh for prerequisites and other information.
+
+source tests/scripts/docker_env.sh
+
+run_in_docker tests/scripts/recursion.pl library/*.c
+run_in_docker tests/scripts/check-generated-files.sh
+run_in_docker tests/scripts/check-doxy-blocks.pl
+run_in_docker tests/scripts/check-names.sh
+run_in_docker tests/scripts/check-files.py
+run_in_docker tests/scripts/doxygen.sh
+
+for compiler in clang gcc; do
+    run_in_docker -e CC=${compiler} cmake -D CMAKE_BUILD_TYPE:String="Check" .
+    run_in_docker -e CC=${compiler} make
+    run_in_docker -e CC=${compiler} make test
+    run_in_docker programs/test/selftest
+    run_in_docker -e OSSL_NO_DTLS=1 tests/compat.sh
+    run_in_docker tests/ssl-opt.sh -e '\(DTLS\|SCSV\).*openssl'
+    run_in_docker tests/scripts/test-ref-configs.pl
+    run_in_docker tests/scripts/curves.pl
+    run_in_docker tests/scripts/key-exchanges.pl
+done
diff --git a/tests/scripts/docker_env.sh b/tests/scripts/docker_env.sh
new file mode 100755
index 0000000..3e1ce61
--- /dev/null
+++ b/tests/scripts/docker_env.sh
@@ -0,0 +1,75 @@
+#!/bin/bash -eu
+
+# docker_env.sh
+#
+# This file is part of mbed TLS (https://tls.mbed.org)
+#
+# Copyright (c) 2018-2019, ARM Limited, All Rights Reserved
+#
+# Purpose
+# -------
+#
+# This is a helper script to enable running tests under a Docker container,
+# thus making it easier to get set up as well as isolating test dependencies
+# (which include legacy/insecure configurations of openssl and gnutls).
+#
+# Notes for users
+# ---------------
+# This script expects a Linux x86_64 system with a recent version of Docker
+# installed and available for use, as well as http/https access. If a proxy
+# server must be used, invoke this script with the usual environment variables
+# (http_proxy and https_proxy) set appropriately.
+#
+# Running this script directly will check for Docker availability and set up
+# the Docker image.
+
+
+# default values, can be overridden by the environment
+: ${MBEDTLS_DOCKER_GUEST:=xenial}
+
+
+DOCKER_IMAGE_TAG="armmbed/mbedtls-test:${MBEDTLS_DOCKER_GUEST}"
+
+# Make sure docker is available
+if ! which docker > /dev/null; then
+    echo "Docker is required but doesn't seem to be installed. See https://www.docker.com/ to get started"
+    exit 1
+fi
+
+# Figure out if we need to 'sudo docker'
+if groups | grep docker > /dev/null; then
+    DOCKER="docker"
+else
+    echo "Using sudo to invoke docker since you're not a member of the docker group..."
+    DOCKER="sudo docker"
+fi
+
+# Build the Docker image
+echo "Getting docker image up to date (this may take a few minutes)..."
+${DOCKER} image build \
+    -t ${DOCKER_IMAGE_TAG} \
+    --cache-from=${DOCKER_IMAGE_TAG} \
+    --build-arg MAKEFLAGS_PARALLEL="-j $(nproc)" \
+    ${http_proxy+--build-arg http_proxy=${http_proxy}} \
+    ${https_proxy+--build-arg https_proxy=${https_proxy}} \
+    tests/docker/${MBEDTLS_DOCKER_GUEST}
+
+run_in_docker()
+{
+    ENV_ARGS=""
+    while [ "$1" == "-e" ]; do
+        ENV_ARGS="${ENV_ARGS} $1 $2"
+        shift 2
+    done
+
+    ${DOCKER} container run -it --rm \
+        --cap-add SYS_PTRACE \
+        --user "$(id -u):$(id -g)" \
+        --volume $PWD:$PWD \
+        --workdir $PWD \
+        -e MAKEFLAGS \
+        -e PYLINTHOME=/tmp/.pylintd \
+        ${ENV_ARGS} \
+        ${DOCKER_IMAGE_TAG} \
+        $@
+}
diff --git a/tests/ssl-opt-in-docker.sh b/tests/ssl-opt-in-docker.sh
new file mode 100755
index 0000000..b3a23fb
--- /dev/null
+++ b/tests/ssl-opt-in-docker.sh
@@ -0,0 +1,52 @@
+#!/bin/bash -eu
+
+# ssl-opt-in-docker.sh
+#
+# This file is part of mbed TLS (https://tls.mbed.org)
+#
+# Copyright (c) 2019, ARM Limited, All Rights Reserved
+#
+# Purpose
+# -------
+# This runs ssl-opt.sh in a Docker container.
+#
+# Notes for users
+# ---------------
+# If OPENSSL_CMD, GNUTLS_CLI, or GNUTLS_SERV are specified the path must
+# correspond to an executable inside the Docker container. The special
+# values "next" and "legacy" are also allowed as shorthand for the
+# installations inside the container.
+#
+# See also:
+# - scripts/docker_env.sh for general Docker prerequisites and other information.
+# - ssl-opt.sh for notes about invocation of that script.
+
+source tests/scripts/docker_env.sh
+
+case "${OPENSSL_CMD:-default}" in
+    "legacy")  export OPENSSL_CMD="/usr/local/openssl-1.0.1j/bin/openssl";;
+    "next")    export OPENSSL_CMD="/usr/local/openssl-1.1.1a/bin/openssl";;
+    *) ;;
+esac
+
+case "${GNUTLS_CLI:-default}" in
+    "legacy")  export GNUTLS_CLI="/usr/local/gnutls-3.3.8/bin/gnutls-cli";;
+    "next")  export GNUTLS_CLI="/usr/local/gnutls-3.6.5/bin/gnutls-cli";;
+    *) ;;
+esac
+
+case "${GNUTLS_SERV:-default}" in
+    "legacy")  export GNUTLS_SERV="/usr/local/gnutls-3.3.8/bin/gnutls-serv";;
+    "next")  export GNUTLS_SERV="/usr/local/gnutls-3.6.5/bin/gnutls-serv";;
+    *) ;;
+esac
+
+run_in_docker \
+    -e P_SRV \
+    -e P_CLI \
+    -e P_PXY \
+    -e GNUTLS_CLI \
+    -e GNUTLS_SERV \
+    -e OPENSSL_CMD \
+    tests/ssl-opt.sh \
+    $@