The idea that sleep could serve a cognitive function has remained popular since Freud stated that dreams were "not nonsense" but a time to sort out experiences [S. Freud, Letter to Wilhelm Fliess, May 1897, in The Origins of Psychoanalysis - Personal Letters of Sigmund Freud, M. Bonaparte, A. Freud, E. Kris (Eds.), Translated by E. Mosbacher, J. Strachey, Basic Books and Imago Publishing, 1954]. Rapid eye movement (REM) sleep, which is associated with dream reports, is now known to be is important for acquisition of some tasks [A. Karni, D. Tanne, B.S. Rubenstein, J.J.M. Askenasy, D. Sagi, Dependence on REM sleep of overnight improvement of a perceptual skill, Science 265 (1994) 679-682; C. Smith, Sleep states and learning: a review of the animal literature, Biobehav. Rev. 9 (1985) 157-168]; although why this is so remains obscure. It has been proposed that memories may be consolidated during REM sleep or that forgetting of unnecessary material occurs in this state [F. Crick, G. Mitchison, The function of dream sleep, Nature 304 (1983) 111-114; D. Marr, Simple memory: a theory for archicortex, Philos. Trans. R. Soc. B. 262 (1971) 23-81]. We studied the firing of multiple single neurons in the hippocampus, a structure that is important for episodic memory, during familiar and novel experiences and in subsequent REM sleep. Cells active in familiar places during waking exhibited a reversal of firing phase relative to local theta oscillations in REM sleep. Because firing-phase can influence whether synapses are strengthened or weakened [C. Holscher, R. Anwyl, M.J. Rowan, Stimulation on the positive phase of hippocampal theta rhythm induces long-term potentiation that can be depotentiated by stimulation on the negative phase in area CA1 in vivo, J. Neurosci. 15 (1977) 6470-6477; P.T. Huerta, J.E. Lisman, Bidirectional synaptic plasticity induced by a single burst during cholinergic theta oscillation in CA1 in vitro, Neuron 15 (1995) 1053-1063; C. Pavlides, Y.J. Greenstein, M. Grudman, J. Winson, Long-term potentiation in the dentate gyrus is induced preferentially on the positive phase of theta-rhythm, Brain Res. 439 (1988) 383-387] this experience-dependent phase shift, which developed progressively over multiple sessions in the environment, is consistent with the hypothesis that circuits may be restructured during REM sleep by selectively strengthening recently acquired memories and weakening older ones.