Some of the disadvantages of geological disposition of nuclear waste materials can be overcome by transmutation of the longest-lived and environmentally most dangerous nuclides into shorter-lived and less toxic ones. This is already being done in some reactors where mixtures containing plutonium isotopes are used as fuel. Transmutation of nuclear waste materials in accelerator-driven subcritical reactor systems would have a number of advantages since it would use accelerator-produced neutrons from the spallation process rather than reactor-produced neutrons from the fission process. This technology has been studied for decades at many laboratories. Until the early 90s, it was not a serious contender for applications because of what appeared to be inherent technical obstacles. During the 90s, however, the need for accelerators producing up to 100 times more powerful proton beams than the most powerful ones in existence and for accurate cross sections at energies up to several orders of magnitude higher than the conventional reactor energy range were being met. Accelerator-driven transmutation technologies also began to gain the support that will be needed to overcome the remaining obstacles as it was gradually realized that geological depositories need to be augmented by other methods of nuclear waste disposition if they are to be practical in the long run. Paramount among the problems that still await a solution is the need for efficient methods of partitioning and separating those radionuclide species that must be re-circulated after each of many necessary irradiations from the shorter-lived ones that can be disposed of at that stage. This problem is far more severe for accelerator-driven reactor systems than for conventional ones partly because the reactions in such systems occur at much higher particle energies and result, therefore, in dozens of radionuclides and a myriad of chemical compounds that are not produced at the lower operation energies of conventional reactors. Recently developed non-aqueous separation methods may offer a solution to this vexing problem, which has caused some scientists, and nuclear chemists in particular, to be highly skeptical of accelerator-driven transmutation technologies as an option to complement other methods of nuclear waste disposition.