Sleep has been implicated with learning and memory in humans and several animal models. The cognitive role of sleep has been postulated to stem from a non-Hebbian rescaling of synaptic weights (synaptic homeostasis hypothesis). Alternatively, sleep has been proposed to trigger a combination of non-Hebbian rescaling and Hebbian upscaling of synaptic weights in complementary circuits (synaptic embossing theory). This talk will review evidence regarding both theories, including changes in neuronal activity, kinase phosphorylation and immediate-early gene expression. In particular, it will show that electrophysiological and molecular changes induced by novel experience fade quickly during sleep in the hippocampus, but persist reverberating for much longer in the neocortex. The hypothesis that anterograde cell plasticity during sleep promotes memory corticalization will be discussed. The talk will also address the cognitive role of dreams, putting into perspective the early psychiatric notion of similarity between dreaming and psychosis. To conclude, recent results regarding the graph-theoretical use of dream reports for quantitative psychiatric diagnosis will be presented.