While sleep appears to be a passive and restful activity, the brain is actually highly active and show an interplay of brain circuits to provide its various stages. During electroencephalography (EEG) experiments in the 1950s that examined brain waves during sleep in human beings, the stages of sleep were discovered.

Going through the first hour of sleep, the brain produces a series of stages during which the brain waves slow down, called slow wave sleep. This period is accompanied by relaxation of the muscles and the eyes. Furthermore, the heart rate, blood pressure and body temperature all fall.
The following half hour the brain generates neocortical EEG waves that are indistinguishable from these observed while awake. At the same time, atonia occurs. This is the paralysis of the muscles in the body (except those that allow breathing of course). This state is called rapid eye movement (REM) sleep. In this period, there is active dreaming and heart rate, blood pressure and body temperature are variable. The first REM period usually lasts 10 to 15 minutes.

These cycles of slow wave and REM sleep alternate during the night, with slow wave sleep becoming more shallow and REM sleep prolonging until the person awakes.

Regulation

During REM sleep, the cholinergic nerves, the thalamus and the cortex are in a state similar to being awake. The brain, however, does not respond very much to external stimuli. This is a consequence of the activity of monoamine nerve cells. These fire rapidly while the person is awake, slow down during slow wave sleep and come to a complete stop during REM sleep.

Arousal from sleep is influenced by two groups of brainstem cells:

One group (in the ventrolateral preoptic nucleus) contains inhibitory neurotransmitters called galanin and GABA. When these neurons fire, they shut off the arousal systems and thus cause sleep.
The second groups of nerve cells (in the lateral hypothalamus) influences and suppresses REM sleep and contains the neurotransmitter orexin, which provides an excitatory signal to the arousal system, particularly to the aforementioned monoamine neurons. Orexin appears to play a critical role in activating the monoamine system and in preventing abnormal transitions. (See also: Fighting off Addiction While Sleeping).

Two main signals control our need for sleep:

Homeostasis: the human body needs to seek an equilibrium of sleep followed by wakefulness. The suggested chemical to drive sleep homeostasis, is called adenosine (Interesting fact: caffeine acts as an adenosine blocker).
Circadian clock: A small group of nerves in the hypothalamus contain ‘clock genes’ that go through a biochemical cycle of roughly 24 hours and thus set the pace for daily cycles of activity.

Source

Brain Facts: A Primer on the Brain and the Nervous System. Society for Neuroscience.