It has been hypothesized that REM (rapid eye movement) sleep has an important role in memory consolidation. The evidence for this hypothesis is reviewed and found to be weak and contradictory. Animal studies correlating changes in REM sleep parameters with learning have produced inconsistent results and are confounded by stress effects. Humans with pharmacological and brain lesion-induced suppression of REM sleep do not show memory deficits, and other human sleep-learning studies have not produced consistent results. The time spent in REM sleep is not correlated with learning ability across humans, nor is there a positive relation between REM sleep time or intensity and encephalization across species. Although sleep is clearly important for optimum acquisition and performance of learned tasks, a major role in memory consolidation is unproven.