The two-process model of sleep regulation posits that the interaction of its two constituent processes, a sleep/wake dependent homeostatic Process S and a circadian Process C, generates the timing of sleep and waking. The time course of Process S was derived from a physiological variable, EEG slow-wave activity. In addition to the timing of sleep, changes of daytime vigilance are accounted for by the interaction of the two processes. The attractiveness of the model derives from its physiological basis and its mathematical simplicity. The two-process model stimulated the establishment of other models of neurobehavioral functions. The background of the model is reviewed and simulations of alertness and sleepiness are discussed.