Although directional antennas have been used in mobile communications systems for quite a long time, realistic applications of directional or smart antennas in wireless ad hoc network have emerged just in recent years. Directional antennas provide numerous benefits, such as higher gains, increased transmission range and low interferences. Wireless medium access schemes play a crucial role in ensuring the efficient and fair sharing of wireless resources. Therefore there are many research work on mechanisms at the wireless medium access layer by using directional antennas. The new features of MAC with directional antennas can cause not only location dependent carrier sensing problems, which have appeared in omnidirectional wireless networks, but also novel issues related to directional antennas. In this paper, an introduction of directional antennas is given. We give a classification of the current wireless MAC protocols using directional antennas. We also present different MAC protocols and compare them. This survey discusses the challenges in the design of these MAC protocols.