Although relatively small in volume, the high-level radioactive wastes contain by far the greatest concentration of radioactivity and emit substantial quantities of heat. This intense radiation and associated decay heat stems largely from the fission products, the majority of which will decay to harmless levels on a timescale of a few hundred years. Consequently, storing the waste for an extended period will not only ensure that it can be monitored and inspected during the time that the radiation and heat output are greatest, but also reduce the thermal load on any eventual underground repository. In this paper consideration is given to the requirements associated with the storage of high-level wastes, and storage concepts are reviewed.