If your cat or dog sleeps with its eyes open, they may have actually closed an eyelid you don't normally notice. That's their third eyelid, or nictitating membrane, and it's virtually transparent. It allows them, and many other animals, to blink and moisten their eyes without losing their vision. It's also found in camels to allow them go through sand storms, and in polar bears which need extra protection against solar radiation and can't afford nice sunglasses instead.