Dark circles, also called Jugo-palpebral grooves are a result of fatigue or age yet, they can also be genetic. Dark circles can steal the riddance look off your face giving you a tired look.
Hollow circles under the eyelid are caused by the disappearance of the fat between the skin of the lower eyelid and the bone in the eye socket. They can, in some cases, extend to the cheekbones (Valley of Tears).