How do I restart Unity

I don't use Unity but given what I know of its mechanics, this should work:

unity

You'll want to stick that in a run box (Alt+F2) rather than a terminal or it'll break when you exit the terminal.

If you want to run it from a terminal use:

setsid unity

I found killall -u USR1 -r -g unity* (optionally, with -i for interactive) to be more effective than @Andrew's answer. My only problem with this vs unity --replace is that it will kill your session which unity --replace doesn't do. So, reserve this for when it is severely broken.

killall -USR1 unity will restart it in an account (USR1) where you have not changed your killall defaults.