Do animals dream?

Regardless of what your Phd is, it's common knowledge that animals sleep. However, it is still unknown if they actually dream.

Sleeping animals, like cats, dogs, and rats, can be seen twitching and "reacting" to things in their sleep. There is a stage of sleep called Rapid Eye Movement (or REM). REM is when your eyeballs  start darting all around, under your closed eyelids. It reflects activity in your brain. Animals go through REM, so it can be speculated that they do dream.