A wide range of alloys have been considered as candidate container materials for the storage and disposal of nuclear waste. The goal of the majority of national nuclear waste management programs is the ultimate disposal of the waste, although, depending upon the strategy being followed, disposal may come only after an extended period of storage. The management strategy depends on the nature of the waste, with intermediate level waste (ILW) generally being stored for a longer period before disposal than is the case for higher activity wastes, such as high-level waste (HLW) from reprocessing activities or spent fuel (SF). This review describes the corrosion issues associated with the storage and disposal of both ILW and HLW/SF. Various factors enter into the decision of which material to select for the container, of which the corrosion behavior in the expected service environment is only one. The corrosion behavior of the container material(s) is closely tied to the nature of the environment to which the containers will be exposed and how that environment changes with time. A general discussion of the corrosion behavior of the materials selected or proposed as container materials is provided, and the specific corrosion issues associated with each class of material highlighted. The classes of material considered for the storage and/or disposal of ILW and HLW/SF include copper, carbon steel and cast iron, stainless steels, titanium alloys, and nickel-based alloys.