If sharks sleep or not is still a mystery as it is very hard to monitor them 24/7. Many sharks need permanent movement in order to breathe. They swim close to the water surface and then get into a resting position and slowly sink again for some time. Then they slowly swim up again and for getting into this resting position again … This is their way to save energy and rest – a bit similar than sleeping.
Other, small, more bottom oriented species who don’t need to swim to breath like the nurse shark or catfish sharks simply go crash on the bottom without moving.
Sharks also have no eyelids. Their eyes are always open.