Traffic density around the globe is increasing on a day-to-day basis, resulting in more accidents, congestion, and pollution. The dynamic vehicular environment induces challenges in designing an efficient and reliable protocol for communication. Timely delivery of safety and non-safety messages is necessary for traffic congestion control and for avoiding road mishaps. For efficient resource sharing and optimized channel utilization, the media access control (MAC) protocol plays a vital role. An efficient MAC protocol design can provide fair channel access and can delay constraint safety message dissemination, improving road safety. This paper reviews the applications, characteristics, and challenges faced in the design of MAC protocols. A classification of the MAC protocol is presented based on contention mechanisms and channel access. The classification based on contention is oriented as contention-based, contention-free, and hybrid, whereas the classification based on channel access is categorized as distributed, centralized, cluster-based, cooperative, token-based, and random access. These are further sub-classified as single-channel and multi-channel, based on the type of channel resources they utilize. This paper gives an analysis of the objectives, mechanisms, advantages/disadvantages, and simulators used in specified protocols. Finally, the paper concludes with a discussion on the future scope and open challenges for improving the MAC protocol design.