Sleep is classically viewed as an all-or-none phenomenon: people are either awake or asleep, either conscious of their environment, immersed in their own dreams or abandoned to a dreamless slumber. Yet, recent finding is humans and animals have shown that, from the brain perspective, the boundaries between wake and sleep can be rather fluid. When we get tired, parts of the brain can fall asleep while others remain awake. Conversely and during sleep itself, the brain can locally wake up. I will present here the electrophysiological evidence of such local aspects of sleep in humans as well as the consequences in terms of sensory processing during both sleep and wakefulness.