In mammals and birds, long episodes of nondreaming sleep ("slow-wave" sleep, SW) are followed by short episodes of dreaming sleep ("rapid-eye-movement" sleep, REM). Both SW and REM sleep have been shown to be important for the consolidation of newly acquired memories, but the underlying mechanisms remain elusive. Here we review electrophysiological and molecular data suggesting that SW and REM sleep play distinct and complementary roles on memory consolidation: While postacquisition neuronal reverberation depends mainly on SW sleep episodes, transcriptional events able to promote long-lasting memory storage are only triggered during ensuing REM sleep. We also discuss evidence that the wake-sleep cycle promotes a postsynaptic propagation of memory traces away from the neural sites responsible for initial encoding. Taken together, our results suggest that basic molecular and cellular mechanisms underlie the reverberation, storage, and propagation of memory traces during sleep. We propose that these three processes alone may account for several important properties of memory consolidation over time, such as deeper memory encoding within the cerebral cortex, incremental learning several nights after memory acquisition, and progressive hippocampal disengagement.