Docker look at the log of an exited container

Is there any way I can see the log of a container that has exited?

I can get the container id of the exited container using docker ps -a but I want to know what happened when it was running.

Use docker logs. It also works for stopped containers and captures the entire STDOUT and STDERR streams of the container's main process:

$ docker run -d --name test debian echo "Hello World"
02a279c37d5533ecde76976d7f9d1ca986b5e3ec03fac31a38e3dbed5ea65def

$ docker ps -a
CONTAINER ID    IMAGE     COMMAND        CREATED             STATUS                     PORTS               NAMES
49daa9d41a24    debian    "echo test"    2 minutes ago       Exited (0) 2 minutes ago                       test

$ docker logs -t test
2016-04-16T15:47:58.988748693Z Hello World

docker logs --tail=50 <container id> for the last fifty lines - useful when your container has been running for a long time.

You can use below command to copy logs even from an exited container :

docker cp container_name:path_of_file_in_container destination_path_locally

Eg:

docker cp sample_container:/tmp/report /root/mylog