Sleep

Melatonin controls sleep in animals

 When a creature sleeps, it periodically releases sleepiness decrease and tiredness decrease in short bursts.
This generally continues until tiredness and sleepiness are removed, and the creature awakens.

See the diagram below.

As it sleeps it is still receptive to certain stimuli, including loud noises, being slapped or tickled.
Sometimes this is enough to stir them, so it's best to leave them alone in peace and quiet!

Dreams

Creatures also have a dream phase, when this happens they become unresponsive to all stimuli, and process their instincts. This means that they treat each instinct as a real-life experience and so learns from it. Each instinct takes approximately five seconds to process.

This means it is a good idea not to overload a creature's genome with too many instinct genes, as it will take a long time for them to become useful.

It is quite normal for a creature to move whilst sleeping, they might sit or stand, shift facing directions, even watch moving objects, although when this happens they will not process dreams, and will awaken easily.

Potential Problems

Be careful when exporting sleeping or especially exhausted creatures,
as this can cause them problems such as temporary Import Coma and potentially lethal Import Shock.

It is generally a good idea to isolate sleeping or sleepy creatures in a warm quiet environment,
and teach them good sleeping habits to improve the processing of instincts and keep them happy.