All sleeping mammals, including dolphins, experience a stage known as REM Sleep.
The dolphin is a voluntary breather even during sleep with the result that veterinary anesthesia of wild dolphins is impossible, as it would result in suffocation of the animal.
It is also known that dolphins sleep only one hemisphere of their brain at a time, thus maintaining enough consciousness to breathe and to watch for possible predators and other threats.
Some dolphins in captivity are recorded to enter a fully asleep stage with both eyes closed. A tail-kick reflex keeping the blowhole above the water is also initialised when under anaesthesia.
The Indus River Dolphin has a sleep method that is different from that of other dolphin species. Living in water with strong currents and potentially dangerous floating debris, it must swim continuously to avoid injury. As a result, this species sleeps in very short bursts, which last between 4 and 60 seconds.