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Both Portainer and Shipyard currently occupy the same space. While there is no Docker Compose support at the moment, however, you can add customisable templates, see https://portainer.readthedocs.io/en/stable/templates.html for more info.

Also, they do eventually plan for Portainer to compete with Rancher https://twitter.com/portainerio/status/814542425410576386

We are adding support for compose YAML files in the Feb/March timeframe.. you will simply upload a yaml file, which portainer will then use to create containers/services

shameless plug, I've developed an HTTP API (plus a minimal web interface) on top of docker compose: https://github.com/francescou/docker-compose-ui , it shold be fully compatible with the docker-compose CLI.