Following a summary of the stages of sleep and wakefulness as monitored with the electroencephalogram and electromyogram, important aspects of the neurophysiology and neuroanatomy of the circuits of vigilance state control are reviewed. A homeostatic drive for sleep and a circadian influence work in concert to determine sleepiness. These processes influence sleep-promoting and central arousing neuronal systems, the former dependent on a group of neurons in the hypothalamic ventrolateral preoptic area and the latter governed by neurons in the pons and basal forebrain. The interactive neuronal circuit that is formed by these cell groups ensures the balance between sleep and wakefulness and the rapid transition to and from sleep. As sleep deepens, the switch to rapid eye movement (REM) sleep occurs. This transition can also be viewed as a balance between one group of pontine neurons that discharge only during REM sleep and another group that cease to discharge during REM sleep. This article concludes with future perspectives based on the recent discovery of the orexin cell group. Orexinergic neurons may be critical both for promoting wakefulness at certain times in the daily cycle and for controlling the switch into REM sleep.