Developing a robust safety case is a key step in the development of a fusion power reactor for electricity generation. Plans for fusion power reactors are already underway and before nuclear facilities are licensed, they must demonstrate they satisfy several safety objectives involving keeping workers and the public safe and limiting any environmental impact. In this paper the key safety issues relating to fusion power are explored, including the current approach to fusion safety and methods of accident identification. The paper draws on major studies on the safety of fusion power plant concepts and the current work being undertaken for the ITER project. As well as discussing the key safety issues and potential accident scenarios, the paper identifies gaps in current knowledge together with areas for future work, including the establishment of internationally recognised safety standards for fusion power stations.