The use of social, anthropomorphic robots to support humans in various industries has been on the rise. During Human-Robot Interaction (HRI), physically interactive non-verbal behaviour is key for more natural interactions. Handshaking is one such natural interaction used commonly in many social contexts. It is one of the first non-verbal interactions which takes place and should, therefore, be part of the repertoire of a social robot. In this paper, we explore the existing state of Human-Robot Handshaking and discuss possible ways forward for such physically interactive behaviours.