The difficulties in disposing of many millions of tons of nuclear waste, comprising radioactive elements with half-lives ranging from microseconds to eons, are discussed, stressing the global nature of the issue. The IAEA classification of nuclear waste into high, intermediate, and low-level forms is described. The classification is based on several factors, including the waste's source and temperature, and half-life: the greater the number of long-lived radioisotopes the waste contains, the higher the level of waste. Although, overall, wastes from commercial power reactors outweigh those from military ones, military programs produce a huge excess of the high-level type. Methods of reprocessing high-level wastes, the solution most favored in Europe, are examined. Opposition to permanent underground disposal sites, the principal alternative to reprocessing, is discussed. Progress in disposing of low-level wastes is described. The technology of vitrification of high-level wastes and of nuclear fuel reprocessing is examined. >