text: Actually cats do go into REM sleep and they do dream - of course we don't know if their subjective experience of the dream is the same as ours, but they do show all the same markers of dreaming that we use to tell when a person is dreaming.  As well as knowing from a scientiffic viewpoint that cats do experience REM sleep, I can also most definitely assure you that they are NOT always constantly aware of their surroundings.  I have on many occasions casually approached my sleeping cat and reached out to pat her, only to have her nealry jump out of her skin because she had no idea I was there! Cats spend a lot of time in slow wave sleep and a lot of time resting but awake, but they do sleep deeply too!