For humans and other land mammals, sleep involves partial or total unconsciousness, the inactivation of all voluntary muscles (those that are consciously controlled) and the suspension of senses such as vision and smell.
Instead, dolphins and other cetaceans undergo an unusual form of sleep called "unihemispheric slow-wave sleep." Also known as deep sleep, slow-wave sleep is a type of sleep thought to help the brain consolidate new memories and recover from its daily activities.
When it's time to rest, a dolphin will shut down only one hemisphere of its brain, and close the opposite eye (the left eye will be closed when the right half of the brain sleeps, and vice versa). During this time, the other half of the brain monitors what's going in the environment and controls breathing functions.