Sleep is an active and regulated process with restorative functions for physical and mental conditions. Based on recordings of brain waves and the analysis of characteristic patterns and waveforms it is possible to distinguish wakefulness and five sleep stages. Sleep and the sleep stages modulate autonomous nervous system functions such as body temperature, respiration, blood pressure, and heart rate. These functions consist of a sympathetic tone usually related to activation and to parasympathetic (or vagal) tone usually related to inhibition. Methods of statistical physics are used to analyze heart rate and respiration to detect changes of the autonomous nervous system during sleep. Detrended fluctuation analysis and synchronization analysis and their applications to heart rate and respiration during sleep in healthy subjects and patients with sleep disorders are presented. The observed changes can be used to distinguish sleep stages in healthy subjects as well as to differentiate normal and disturbed sleep on the basis of heart rate and respiration recordings without direct recording of brain waves. Of special interest are the cardiovascular consequences of disturbed sleep because they present a risk factor for cardiovascular disorders such as arterial hypertension, cardiac ischemia, sudden cardiac death, and stroke. New derived variables can help to find indicators for these health risks.