Prior to 1951, it was thought our brains had an on off switch that automatically made us sleep and wake up.
That was until Nathaniel Kleitman's research into sleep and dreaming began to unravel the mystery of what happens when we cross over to this other realm.
Sixty six years later we now know there are five stages of sleep; well 4 plus the REM sleep stage. Some scientists often cite just 3, combining stages 3 & 4 in one and adding on REM sleep as a separate entity.
The following diagram explains each stage (take note of how brainwave activity changes during each stage):
For a better understanding of how sleep cycles work, what happens to your brainwaves when you sleep, and why we sleep the way we do, click here and read this article.