Two-step theories of memory formation suggest that an initial encoding stage, during which transient neural assemblies are formed in the hippocampus, is followed by a second step called consolidation, which involves re-processing of activity patterns and is associated with an increasing involvement of the neocortex. Several studies in human subjects as well as in animals suggest that memory consolidation occurs predominantly during sleep (standard consolidation model). Alternatively, it has been suggested that consolidation may occur during waking state as well and that the role of sleep is rather to restore encoding capabilities of synaptic connections (synaptic downscaling theory). Here, we review the experimental evidence favoring and challenging these two views and suggest an integrative model of memory consolidation.