Recent advances in self-interference cancellation techniques enable in-band full-duplex (FD) transmission in which a wireless node can simultaneously transmit and receive in the same frequency band. However, to fully exploit the benefits of FD technology in a wireless network, in addition to the physical (PHY) layer issues, medium access control (MAC) layer issues such as inter-node collisions, fairness between half-duplex (HD) and FD users, opportunistic selection of different modes of FD transmission, and synchronization issues need to be resolved. To this end, this article first discusses the fundamental concepts, potential benefits, and primary network topologies of FD transmission. We then highlight immediate challenges (both in the PHY and MAC layers) that need to be addressed in designing FD wireless systems. A qualitative comparison among the existing full-duplex MAC (FD-MAC) protocols is then provided. Finally, the primary requirements and research issues for the design of FD-MAC protocols are discussed, and implications of FD technology in cellular wireless networks are highlighted.