Sleep function remains elusive despite our rapidly increasing comprehension of the processes generating and maintaining the different sleep stages. Several lines of evidence support the hypothesis that sleep is involved in the off-line reprocessing of recently-acquired memories. In this review, we summarize the main results obtained in the field of sleep and memory consolidation in both animals and humans, and try to connect sleep stages with the different memory systems. To this end, we have collated data obtained using several methodological approaches, including electrophysiological recordings of neuronal ensembles, post-training modifications of sleep architecture, sleep deprivation and functional neuroimaging studies. Broadly speaking, all the various studies emphasize the fact that the four long-term memory systems (procedural memory, perceptual representation system, semantic and episodic memory, according to Tulving's SPI model; Tulving, 1995) benefit either from non-rapid eye movement (NREM) (not just SWS) or rapid eye movement (REM) sleep, or from both sleep stages. Tulving's classification of memory systems appears more pertinent than the declarative/non-declarative dichotomy when it comes to understanding the role of sleep in memory. Indeed, this model allows us to resolve several contradictions, notably the fact that episodic and semantic memory (the two memory systems encompassed in declarative memory) appear to rely on different sleep stages. Likewise, this model provides an explanation for why the acquisition of various types of skills (perceptual-motor, sensory-perceptual and cognitive skills) and priming effects, subserved by different brain structures but all designated by the generic term of implicit or non-declarative memory, may not benefit from the same sleep stages.