Long-term memory formation is a major function of sleep. Based on evidence from neurophysiological and behavioral studies mainly in humans and rodents, we consider the formation of long-term memory during sleep as an active systems consolidation process that is embedded in a process of global synaptic downscaling. Repeated neuronal replay of representations originating from the hippocampus during slow-wave sleep leads to a gradual transformation and integration of representations in neocortical networks. We highlight three features of this process: (i) hippocampal replay that, by capturing episodic memory aspects, drives consolidation of both hippocampus-dependent and non-hippocampus-dependent memory; (ii) brain oscillations hallmarking slow-wave and rapid-eye movement sleep that provide mechanisms for regulating both information flow across distant brain networks and local synaptic plasticity; and (iii) qualitative transformations of memories during systems consolidation resulting in abstracted, gist-like representations.