To assist in the development of nuclear fusion as a viable commercial power source, preparation is underway for the fusion demonstration reactor (DEMO), which will build on the work of ITER, the international experimental fusion reactor. Like other advanced nuclear energy systems, DEMO must satisfy several goals including a high level of public and worker safety, low environmental impact, high reactor availability, a closed fuel cycle and the potential to be economically competitive. Yet there are still large scientific and technological safety gaps between the on-going ITER project and DEMO that will need to be addressed. Here we review international fusion safety research and development relevant to DEMO, following the lessons learned so far from ITER. We identify the main scientific and technological safety gaps, drawing on knowledge from the development of fission energy, in particular Generation IV (Gen-IV) fission reactors. From this survey, we discuss the corresponding implications for the design and operation of DEMO.