Sleep is ubiquitous among the animal realm, and represents about 30% of our lives. Despite numerous efforts, the reason behind our need for sleep is still unknown. The Theory of neuronal Cognition (TnC) proposes that sleep is the period of time during which the local inhibitory synapses (in particular the cortical ones) are replenished. Indeed, as long as the active brain stays awake, hebbian learning guarantees that efficient inhibitory synapses lose their efficiency – just because they are efficient at avoiding the activation of the targeted neurons. Since hebbian learning is the only known mechanism of synapse modification, it follows that to replenish the inhibitory synapses’ efficiency, source and targeted neurons must be activated together. This is achieved by a local depolarization that may travel (wave). The period of time during which such slow waves are experienced has been named the ‘‘slow-wave sleep’’ (SWS). It is cut into several pieces by shorter periods of paradoxical sleep (REM) which activity resembles that of the awake state. Indeed, SWS – because it only allows local neural activation – decreases the excitatory long distance connections strength. To avoid losing the associations built during the awake state, these long distance activations are played again during the REM sleep. REM and SWS sleeps act together to guarantee that when the subject awakes again, his inhibitory synaptic efficiency is restored and his (excitatory) long distance associations are still there.