Here's a great video from Amazon re:Invent on running Docker in production.
From the session description:
In this session, we will learn how to define and run multi-container applications with Docker Compose. Then, we will show how to deploy and scale them seamlessly to a cluster with Docker Swarm; and how Amazon EC2 Container Service (ECS) eliminates the need to install, operate, and scale your own cluster management infrastructure. We will also walk through some best practice patterns used by customers for running their microservices platforms or batch jobs. Sample code and Compose templates will be provided on GitHub afterwards.