How do some species of dolphin manage to sleep and breath air at the same time?

Surprisingly, dolphins can't breath underwater. They are mammals, just like humans and need air to breath. That's why they have a blowhole on the top of their head which they get air from.

To go to sleep they turn half os their brain off to rest then the other half stays awake to concentrate on breathing and using their blowhole. Then, when that half is rested the other half goes to sleep while the one awake concentrates on breathing and using their blowhole.