Children usually move quickly on to reach (within about five minutes) slow wave sleep, that is stage 3 and 4 sleep. They are now very deeply asleep, and difficult to rouse. (Parents all know when children are in deep slow-wave sleep - it's when you can carry them out of the car and put them to bed without waking them.) Although much of the brain seems to close down during slow-wave sleep, parts are still active, processing new information. In children, slow-wave sleep is also important for physical development, being the time at which growth hormone secretion reaches its peak.
A phase of slow-wave sleep lasts about 80 minutes; after that, sleepers rise back up through the four levels to a state much closer to consciousness. This is called REM sleep (rapid eye movement - because the eyes dart about beneath the eyelids), and it's here that most dreams seem to occur. Brain activity is much higher in REM sleep than slow-wave sleep, especially the areas of the brain associated with emotion.
During the night, sleepers move through four or five sleep cycles - dropping down into deep slow-wave sleep and drifting up into REM sleep.
They spend longer in slow-wave sleep during the first half of the night, but in the second half of the night they get more REM sleep. Babies and younger children seem to spend more time in REM sleep than adults - which could well be connected with infants' greater concentration on procedural learning.