In the Automation view, you will se when the automation was last run in the Status column. More detailed history of the runs can be found under menu --> History.
In this view, you'll se the last 500 events of the automation. Every automation can have one or several events.
The list will show you when the event happened, what user triggered it, what event it was, and the status of it. If any of the events encounter an error, the status will change to "Failed" and a error message will appear with more information.