This paper summarizes the present knowledge about the cellular bases of the sleep K-complex (KC). The KC has two phases: the initial surface-positive wave is due to the synchronous excitation of cortical neurones, while the subsequent surface-negative wave represents neuronal hyperpolarization. These variations of membrane potential occur within a slow (<1 Hz) oscillation that characterizes all sleep stages. Therefore, KCs are periodic, and their shape and frequency are modulated by the increasing degree of deafferentation attained by the corticothalamic network with the deepening of the sleep. Within this network, the rhythmic KCs recurring at the frequency of the slow oscillation play a leading role by triggering and grouping other sleep oscillations, such as spindles (7-14 Hz) and delta (1-4 Hz). The KC is mainly a spontaneous event generated in cortical networks. During nocturnal epileptic seizures, the KCs are precursors of paroxysmal spike-wave complexes.