To run Wayland applications in docker, you need an already running Wayland compositor like Gnome-Wayland or Weston.

• Wayland compositors normally provide an X display with Xwayland, too. You can share access to Xwayland the same way as access to regular Xorg.
• You have to share the Wayland socket. You find it in XDG_RUNTIME_DIR and its name is stored in environment variable WAYLAND_DISPLAY.
• XDG_RUNTIME_DIR only allows access for its owner, so you need the same user in container as on host.
• Example similar to x11docker option --hostwayland:

docker run -e XDG_RUNTIME_DIR=/tmp \
           -e WAYLAND_DISPLAY=$WAYLAND_DISPLAY \
           -v $XDG_RUNTIME_DIR/$WAYLAND_DISPLAY:/tmp/$WAYLAND_DISPLAY  \
           --user=$(id -u):$(id -g) \
           imagename waylandapplication

• QT5 applications also need -e QT_QPA_PLATFORM=wayland and must be started with imagename dbus-launch waylandapplication.
• You can combine Wayland access and X access to provide both to docker container.
  • You can indicate that you prefer Wayland with -e XDG_SESSION_TYPE=wayland
• Collection of Wayland related environment variables for different toolkits:
  • GTK: GDK_BACKEND=wayland
  • QT5: QT_QPA_PLATFORM=wayland
  • Clutter/GTK3: CLUTTER_BACKEND=wayland
  • SDL: SDL_VIDEODRIVER=wayland
  • E / Enlightenment: ELM_DISPLAY=wl ELM_ACCEL=opengl ECORE_EVAS_ENGINE=wayland_egl