A social robot acting as a 'mediator' can enhance interactions between humans, for example, in fields such as education and healthcare. A particularly promising area of research is the use of a social robot mediator in a multiparty setting, which tends to be the most applicable in real-world scenarios. However, research in social robot mediation for multiparty interactions is still emerging and faces numerous challenges. This paper provides an overview of social robotics and mediation research by highlighting relevant literature and some of the ongoing problems. The importance of incorporating relevant psychological principles for developing social robot mediators is also presented. Additionally, the potential of implementing a Theory of Mind in a social robot mediator is explored, given how such a framework could greatly improve mediation by reading the individual and group mental states to interact effectively.