When we sleep, we go through five sleep stages. The first stage is a very light sleep from which it is easy to wake up. The second stage moves into a slightly deeper sleep, and stages three and four represent our deepest sleep. Our brain activity throughout these stages is gradually slowing down so that by deep sleep, we experience nothing but delta brain waves -- the slowest brain waves (see "Brain Waves" sidebar). About 90 minutes after we go to sleep and after the fourth sleep stage, we begin REM sleep. Rapid eye movement (REM) was discovered in 1953 by University of Chicago researchers Eugene Aserinsky, a graduate student in physiology, and Nathaniel Kleitman, Ph.D., chair of physiology. REM sleep is primarily characterized by movements of the eyes and is the fifth stage of sleep.