Electroencephalographic slow-wave activity (EEG SWA) is an electrophysiological signature of slow (0.5 to 4.0 Hz), synchronized, oscillatory neocortical activity. In healthy individuals, EEG SWA is maximally expressed during non-rapid-eye-movement (non-REM) sleep, and intensifies as a function of prior wake duration. Many of the cellular and network mechanisms generating EEG SWA have been identified, but a number of questions remain unanswered. For example, although EEG SWA is a marker of sleep need, its precise relationship with sleep homeostasis and its roles in the brain are unknown. In this review, the authors discuss their current understanding of the neural mechanisms and possible functions of EEG SWA.