Does rapid eye movement during sleep reveal where you’re looking at in the scenery of dreams, or are they simply the result of random jerks of our eye muscles? Since the discovery of REM sleep in the early 1950s, the significance of these rapid eye movements has intrigued and fascinated scores of scientists, psychologists and philosophers. REM sleep, as the name implies, is a period of sleep when your eyes move under your closed eyelids. It’s also the period when you experience vivid dreams.