Sleep and waking have been traditionally considered global behavioural states regulated by subcortical neuromodulatory circuits in a top-down fashion. Over the last years, we have been experiencing a paradigm shift towards a view that both wake and sleep are in essence local processes. Here we review recent clinical and basic research works supporting this view by taking advantage of stereotactic electroencephalography (Stereo-EEG, SEEG) recordings performed in epileptic patients. Specifically, we will discuss a growing body of evidence showing how electrophysiological features of sleep and wakefulness are coexisting across diffuse brain areas in pathological and physiological sleep as well as during state transitions (sleep onset and awakenings). Finally, we will discuss their implication for sleep medicine to extent that, reconsidering the classical definition of wakefulness and sleep as separate and mutually exclusive states may offer new insight for the understanding of parasomnias and other dissociated states.