Whales sleep about 8 hours each day. Whales don't go into a deep sleep like we do, because they have to be partially conscious to breathe. Whales are able to partly sleep by letting one half of their brain sleep at a time. This is called unihemispherical sleeping.
When they dive, their heart beats more slowly and select arteries are constricted. This slows the flow of blood to certain organs without decreasing blood pressure.