Different challenges, constraints for quality of sleep and wakefulness, sleep in extreme conditions, search for a better identification of disorders of sleep and wakefulness, spur researches on the circadian rhythm of sleep and on its disorders. Any advance in that field rests on the understanding of different physiologic phenomena: the intrinsic period of our internal clock is not 24-hours but a little less than 25-hours and it must be reset daily by the Zeitgebers. A sudden phase shift provokes an external desynchronisation. In addition not all rhythms resynchronize together resulting in an internal desyncronization. There is a close relationship between quantities of total sleep and REM sleep and the time of sleep onset within the 24-hours. The propensity to sleep follows a circasemidian rhythm with a major peak during the night and a secondary peak in the midafternoon. Disorders of the circadian rhythm of sleep are of two types: related to the misalignment of the sleep-wake schedule and the synchronizer-controlled rest-activity rhythm (shift work sleep disorder and time zone change syndrome) or related to an abnormal escape of the individual rest-activity rhythm from synchronizer control (delayed sleep phase syndrome, advanced sleep phase syndrome and non 24-hour sleep-wake syndrome.