Terahertz communication is emerging as a future technology to support Terabits per second link with highlighting features as high throughput and negligible latency. However, the unique features of the Terahertz band such as high path loss, scattering and reflection pose new challenges and results in short communication distance. The antenna directionality, in turn, is required to enhance the communication distance and to overcome the high path loss. However, these features in combine negate the use of traditional Medium access protocols. Therefore novel MAC protocol designs are required to fully exploit their potential benefits including efficient channel access, control message exchange, link establishment, mobility management, and line-of-sight blockage mitigation. An in-depth survey of Terahertz MAC protocols is presented in this paper. The paper highlights the key features of the Terahertz band which should be considered while designing an efficient Terahertz MAC protocol, and the decisions which if taken at Terahertz MAC layer can enhance the network performance. Different Terahertz applications at macro and nano scales are highlighted with design requirements for their MAC protocols. The MAC protocol design issues and considerations are highlighted. Further, the existing MAC protocols are also classified based on network topology, channel access mechanisms, and link establishment strategies as Transmitter and Receiver initiated communication. The open challenges and future research directions on Terahertz MAC protocols are also highlighted.