Even though sharks need to keep water moving over their gills to receive oxygen, some sharks need to keep moving to do this, while others don't. Either way, sharks, like other marine animals, don't seem to fall in a deep sleep like we do.
Some sharks have spiracles, a small opening behind their eyes, that force water across the shark’s gills so the shark can be still when it rests.
Other sharks do need to swim constantly to keep water moving over their gills and their bodies. These sharks have active periods, and restful periods, rather than undergoing deep sleep like we do. They seem to be “sleep swimming,” with parts of their brain less active, or "resting," while the shark remains swimming.