During the past two decades, robots have been increasingly deployed in games. Researchers use games to better understand human-robot interaction and, in turn, the inclusion of social robots during gameplay creates new opportunities for novel game experiences. The contributions from social robotics and games communities cover a large spectrum of research questions using a wide variety of scenarios. In this article, we present the first comprehensive survey of the deployment of robots in games. We organise our findings according to four dimensions: (1) the societal impact of robots in games, (2) games as a research platform, (3) social interactions in games, and (4) game scenarios and materials. We discuss some significant research achievements and potential research avenues for the gaming and social robotics communities. This article describes the state of the art of the research on robots in games in the hope that it will assist researchers to contextualise their work in the field, to adhere to best practices and to identify future areas of research and multidisciplinary collaboration.