Sleep in humans, and similarly in rodents, consists of the alternating occurrence of non-rapid eye movement (NonREM) sleep periods and intermittent REM sleep periods (Fig. 1). The deepest kind of NonREM sleep is termed slow wave sleep (SWS). For a long time, sleep-associated memory processing was suspected to take place mainly during REM sleep, probably because in human subjects awakenings from this sleep stage are usually associated with the report of vivid dreams. However, approaches using selective REM sleep deprivation to test possible memory consolidating effects of this sleep stage revealed overall rather mixed results