Dolphins do sleep with one eye open, a skill that is necessary for survival. When dolphins sleep, only half of their brains shut down, which enables them to remain vigilant to the threat of predators and to regulate their breathing to avoid drowning.
Scientists from the U.S. Navy Marine Mammal Program conducted experiments designed to determine if sleep deprivation affected dolphins due to their split-brain habit of sleeping in shifts. Following five days of testing, the dolphins were as alert and responsive as before the experiment began with no noticeable effects on their health or mental dexterity. The results also revealed that information observed from the non-sleeping half of the brain filters to the sleeping side of the brain.