Effective approaches to the management of plutonium and highly enriched uranium (HEU)-the essential ingredients of nuclear weapons-are fundamental to controlling nuclear proliferation and providing the basis for deep, transparent, and irreversible reductions in nuclear weapons stockpiles. The collapse of the Soviet Union and the ongoing dismantlement of tens of thousands of nuclear weapons are creating unprecedented stresses on the systems for managing these materials, as well as unprecedented opportunities for cooperation to improve these systems. In this article, we summarize the technical background to this situation, and the current and prospective security challenges posed by military stockpiles of these materials in the United States and Russia. We then review the programs in place to address these challenges, the progress of these programs to date, and the work remaining to be done, in five areas: (a) preventing theft and smuggling of nuclear warheads and fissile materials; (b) building a regime of monitored reductions in nuclear warhead and fissile material stockpiles; (c) ending further production of excess fissile materials; (d) reducing stockpiles of excess fissile materials; and (e) avoiding economic collapse in the nuclear cities where substantial fractions of these materials and their guardians reside.