Non-REM sleep deprivation and REM sleep deprivation both lead to specific rebounds, suggesting that these states fulfil physiological needs. In view of impaired performance after sleep deprivation, a recovery function of sleep seems likely. The timing of this recovery is restricted to a narrow time interval within the 24 hour day, i.e. the night. Generally, nocturnal sleep in humans is considered a consequence of the impact of the circadian pacemaker in the hypothalamus on sleep propensity. The interaction between the homeostatic recovery process and the circadian pacemaker has been modelled in the two-process model of sleep regulation. This model is used as a starting point in the present review. A series of refinements and several alternative models are discussed, both with respect to the quality of fit of theory and data, as well as with respect to the concepts behind the models.