Since the discovery of REM (Rapid Eye Movement) sleep in 1953, misconceptions have arisen as to the evidence for its adaptive function and its relation to dreams. Eye movements recorded during REM sleep have not been consistently reported to mirror the eye movements predicted by dream reports. But evidence on eye movement and somatic motor expression from patients with REM sleep behavior disorder (RBD) is consistent with dream enacting behavior. The assumption that dreaming occurs only in REM sleep is incorrect, with numerous reports of nonREM dreaming. However, there may be qualitative differences between REM and nonREM dreams. Early studies that suggested a vital role for REM sleep in psychological well-being are refuted by studies of pharmacologically induced partial or complete REM sleep suppression. Studies of sleep across species show that the primitive monotreme mammals, platypus and echidna, have far more REM sleep than any other homeotherm group, whereas birds have far less REM sleep than any other homeotherm group. Human REM sleep amounts are not unusual, are correlated with nonREM sleep durations but are not correlated with intelligence. Across groups of homeotherms, REM sleep time is highly and inversely correlated (r=–0.975, P=0.02) with average core body temperature, suggesting that REM sleep cycles with nonREM sleep to regulate brain temperature during sleep. Cetacean mammals (dolphins and whales) do not have REM sleep despite their very large brain sizes and impressive cognitive abilities. Reports of “REM sleep-like states” in arachnids, cephalopods and in zebrafish larvae are lacking critical evidence that the observed behaviors are occurring during sleep and that the behaviors are homologous to mammalian REM sleep.