All our lives, we alternate between wakefulness and sleep with direct consequences on our ability to interact with our environment, the dynamics and contents of our subjective experience, and our brain activity. Consequently, sleep has been extensively characterised in terms of behavioural, phenomenological, and physiological changes, the latter constituting the gold standard of sleep research. The common view is thus that sleep represents a collection of discrete states with distinct neurophysiological signatures. However, recent findings challenge such a monolithic view of sleep. Indeed, there can be sharp discrepancies in time and space in the activity displayed by different brain regions or networks, making it difficult to assign a global vigilance state to such a mosaic of contrasted dynamics. Viewing sleep as a multidimensional continuum rather than a succession of non-overlapping and mutually exclusive states could account for these local aspects of sleep. Moving away from the focus on sleep states, sleep can also be investigated through the brain processes that are present in sleep, if not necessarily specific to sleep. This focus on processes rather than states allows to see sleep for what it does rather than what it is, avoiding some of the limitations of the state perspective and providing a powerful heuristic to understand sleep. Indeed, what is sleep if not a process itself that makes up wake up every morning with a brain cleaner, leaner and less cluttered.