A survey of recent developments in the field of plutonium disposal by the application of advanced nuclear systems, both critical and subcritical. Current national R&D plans are summarized. The actinide-fuelled critical reactors are associated with control problems, since they tend to have a small delayed neutron fraction coupled with a small Doppler effect and a positive void coefficient. Current thinking is turning to accelerator-driven subcritical systems for the transmutation of actinides. The book's conclusion is that the various systems proposed are technically feasible, even though not yet technically mature. The book presents a unique summary and evaluation of all relevant possibilities for burning surplus plutonium, presented by experts from a variety of different disciplines and interests, including the defence establishment. The obvious issue - the non-proliferation of nuclear weapons - is vital, but the matter represents a complex technological challenge that also requires an assessment in economic terms.