According to the two-process model of sleep regulation, the timing and structure of sleep are determined by the interaction of a homeostatic and a circadian process. The original qualitative model was elaborated to quantitative versions that included the ultradian dynamics of sleep in relation to the non-REM-REM sleep cycle. The time course of EEG slow-wave activity, the major marker of non-REM sleep homeostasis, as well as daytime alertness were simulated successfully for a considerable number of experimental protocols. They include sleep after partial sleep deprivation and daytime napping, sleep in habitual short and long sleepers, and alertness in a forced desynchrony protocol or during an extended photoperiod. Simulations revealed that internal desynchronization can be obtained for different shapes of the thresholds. New developments include the analysis of the waking EEG to delineate homeostatic and circadian processes, studies of REM sleep homeostasis, and recent evidence for local, use-dependent sleep processes. Moreover, nonlinear interactions between homeostatic and circadian processes were identified. In the past two decades, models have contributed considerably to conceptualizing and analyzing the major processes underlying sleep regulation, and they are likely to play an important role in future advances in the field.
