According to a widely held concept, the formation of long-term memories relies on a reactivation and redistribution of newly acquired memory representations from temporary storage to neuronal networks supporting long-term storage. Here, we review evidence showing that this process of system consolidation takes place preferentially during sleep as an 'off-line' period during which memories are spontaneously reactivated and redistributed in the absence of interfering external inputs. Moreover, postlearning sleep leads to a reorganization of neuronal representations and qualitative changes of memory content. We propose that memory reactivations during sleep are accompanied by a transient destabilization of memory traces. Unlike wake reactivations that form part of an updating of memories with respect to current perceptual input, reactivations during sleep allow for gradually adapting newly acquired memories to pre-existing long-term memories whereby invariants and certain other features of these memories become extracted.