Kitty REM sleep

I never noticed it before like this, but boy my cat has some intense REM sleeps at times. He was moving his head and his little paws were twitching.
He also made some slirping sounds. Do they dream like people do you think? Was he in a planet of just mice only?

I havn't looked into the subject too deep, but they do say that animals do dream like humans. I can't imagine what they dream about...lol.

They must have all sorts of adventures like chasing mice and things. I know mine start licking and chewing and twitching their legs and whiskers.