Sleep is not just the absence of wakefulness but a regulated process with an important restorative function. Based on electroencephalographic recordings and characteristic patterns and waveforms we can distinguish wakefulness and five sleep stages grouped into light sleep, deep sleep, and rapid-eye-movement (REM) sleep. In order to explore the functions of sleep and sleep stages, we investigated the dynamics of sleep stages over the night and of heart-rate variability during the different sleep stages. Sleep stages and intermediate wake states have different distributions of their duration and this allows us to create a model for the temporal sequence of sleep stages and wake states. Heart rate is easily accessed with a high precision by the recording and analysis of the electrocardiogram (ECG). Heart-rate regulation is part of the autonomous nervous system and sympathetic tone is strongly influenced by the sleep stages.