Fusion power holds the promise of electricity production with a high degree of safety and low environmental impact. Favourable characteristics of fusion as an energy source provide the potential for this very good safety and environmental performance. But to fully realize the potential, attention must be paid in the design of a demonstration fusion power plant (DEMO) or a commercial power plant to minimize the radiological hazards. These hazards arise principally from the inventory of tritium and from materials that become activated by neutrons from the plasma. The confinement of these radioactive substances, and prevention of radiation exposure, are the primary goals of the safety approach for fusion, in order to minimize the potential for harm to personnel, the public, and the environment. The safety functions that are implemented in the design to achieve these goals are dependent on the performance of a range of materials. Degradation of the properties of materials can lead to challenges to key safety functions such as confinement. In this paper the principal types of material that have some role in safety are recalled. These either represent a potential source of hazard or contribute to the amelioration of hazards; in each case the related issues are reviewed. The resolution of these issues lead, in some instances, to requirements on materials specifications or to limits on their performance.