A Mobile Social Network (MSN) consists of nodes that are related socially, in addition to their physical connection through wireless links. In terms of mobile devices, social connection reflects the frequency of encounter, so that the users of these devices are socially connected if they communicate with each other frequently. This layer of social connectivity, combined with the physical connectivity of being in the communication range of each other, can help improve the routing performance. However, it also inherits the challenges of mobile adhoc networks. These challenges include the limited energy resource, intermittent connectivity, and the limited storage. To overcome these challenges and improve routing efficiency, social metrics are exploited to carefully choose the candidate relays in MSNs. In this paper, we review the routing protocols proposed or candidate to be implemented in MSN, focusing on the routing metrics used to select the candidate relays. In addition, we describe a list of performance measures that are useful in comparing current and future MSN routing protocols.