We review current models of consciousness in the context of wakefulness and sleep. We show that recent results on Slow Wave Sleep, including our own works, naturally fit within consciousness models. In particular, Sleep Slow Oscillations, namely low-frequency (<1Hz) oscillations, contain electrophysiological properties (up and down states) able to elicit and quench neural integration during Slow Wave Sleep. The physiological unconsciousness related to the Sleep Slow Oscillation derives from the interplay between spontaneous or evoked wake-like activities (up states) and half-a-second's electrical silences (down states). Sleep Slow Oscillation induces unconsciousness via the formation of parallel and segregated neural activities.