With the advances in technology, Underwater Acoustic Sensor Networks (UW-ASNs) will make it possible to explore and observe the ocean, which covers two-thirds of the Earth's surface. Unlike terrestrial sensor networks, UW-ASNs use acoustic links to explore natural undersea resources and gather scientific data in collaborative monitoring missions. By using the acoustic wave as a means of communication, UW-ASNs are inherently confronted with long and variable propagation delay and high transmission power consumption. These limitations can be overcome by sharing the limited channel resources in an efficient and reliable manner, which can be done by carefully designing MAC protocols. In this survey, we review the unique aspects of UW-ASNs in detail and existing MAC protocols. Finally, we suggest future directions for research on UW-A MAC protocols.