Device-to-device (D2D) communication is one of the most recent advancements in wireless communication technology. It was introduced in cellular communication technology by the 3rd Generation Partnership Project (3GPP) to lay a foundation for the evolving 5G architecture. It has now emerged as a promising technology for proximate devices. It enables proximate devices to communicate directly without the involvement of a third party network infrastructure. Researchers are analysing various methods to facilitate the smooth integration of D2D communication technology into the existing network system architecture. This paper lists all the different possible modes of operation in D2D communication based on the varying use-case scenarios and highlights the security and privacy requirements for D2D communication. Some of the recent authentication proposals for D2D communication technology are further reviewed, and their security and privacy capabilities are analysed. Apart from authentication, we also reviewed some recent proposals of access control in D2D and highlighted the security issues addressed. We then identified the open issues that prevail in implementing D2D technology in a real-world scenario for future researchers, emphasising the existing authentication and access control techniques in D2D communication.