The human body is an extremely challenging environment for the operation of wireless communications systems, not least because of the complex antenna-body electromagnetic interaction effects which can occur. This is further compounded by the impact of movement and the propagation characteristics of the local environment which all have an effect upon body centric communications channels. As the successful design of body area networks (BANs) and other types of body centric system is inextricably linked to a thorough understanding of these factors, the aim of this paper is to conduct a survey of the current state of the art in relation to propagation and channel models primarily for BANs but also considering other types of body centric communications. We initially discuss some of the standardization efforts performed by the Institute of Electrical and Electronics Engineers 802.15.6 task group before focusing on the two most popular types of technologies currently being considered for BANs, namely narrowband and Ultrawideband (UWB) communications. For narrowband communications the applicability of a generic path loss model is contended, before presenting some of the scenario specific models which have proven successful. The impacts of human body shadowing and small-scale fading are also presented alongside some of the most recent research into the Doppler and time dependencies of BANs. For UWB BAN communications, we again consider the path loss as well as empirical tap delay line models developed from a number of extensive channel measurement campaigns conducted by research institutions around the world. Ongoing efforts within collaborative projects such as Committee on Science and Technology Action IC1004 are also described. Finally, recent years have also seen significant developments in other areas of body centric communications such as off-body and body-to-body communications. We highlight some of the newest relevant research in these areas as well as discussing some of the advanced topics which are currently being addressed in the field of body centric communications.