The importance of nuclear powered electricity generation in helping to solve Canada's future energy requirements is well documented. It is also well known that whereas nuclear reactors are technically feasible, they also involve serious human and environmental problems which remain to be solved. One problem is safe disposal of the various types of radioactive wastes. Mining waste and mill tailings containing toxic radium are produced in large quantities. It is believed about 80 million tonnes have already accumulated at Elliot Lake, Ontario, alone and that this may increase by the year 2000 to several hundred million tonnes. These tailings are large in bulk but relatively low in radioactivity. Wastes from nuclear generating stations, on the contrary, are highly radioactive but relatively small in volume. This report provides a brief overview of how electricity is generated by means of nuclear power, and gives reasons which render safe disposal of high-level nuclear wastes a particularly difficult and multifaceted problem. It is suggested that under Canadian conditions deep underground burial of these wastes in mined-out facilities within igneous rocks is the most acceptable solution.