A symposium was organized to reexamine the realities of vertical proliferation between the United States and the Soviet Union and to place into perspective the horizontal proliferation of nuclear weapons throughout the world, including the possible role of commercial nuclear power in facilitating proliferation. The four invited symposium presentations are provided in this monograph. They include: "Nuclear Power and Nuclear Weapons: The Connection Is Tenuous" (Bernard I. Spinrad); "Nuclear Power and Nuclear Weapons: The Connection Is Dangerous" (John P. Holdren); "Horizontal Proliferation: The Spread of Nuclear Weapons to Other Countries" (Gene I. Rochlin); and "Vertical Proliferation: The Nuclear Arms Race of the Superpowers" (Herbert F. York). Among the areas/issues addressed in the first three papers are: weapons efficacy of materials from nuclear power reactors; nuclear power and world tension; nuclear policy alternatives; motivations and barriers (technical, economic, political) to acquiring nuclear weapons; history of power-related proliferation and prospects for further proliferation; Nuclear Non-Proliferation Treaty (NPT); gradual erosion of the NPT regime; and future of NPT safeguards. The final paper reviews facts/data about the arms race, describes systematic relationships among the facts/data, and draws conclusions based on the relationships. (JN)