Nuclear disarmament is firmly back on the international agenda. But almost all current thinking on the subject is focused on the process of reducing the number of weapons from thousands to hundreds. This rigorous analysis examines the challenges that exist to abolishing nuclear weapons completely, and suggests what can be done now to start overcoming them. The paper argues that the difficulties of "getting to zero" must not preclude many steps being taken in that direction. It thus begins by examining steps that nuclear-armed states could take in cooperation with others to move towards a world in which the task of prohibiting nuclear weapons could be realistically envisaged. The remainder of the paper focuses on the more distant prospect of prohibiting nuclear weapons, beginning with the challenge of verifying the transition from low numbers to zero. It moves on to examine how the civilian nuclear industry could be managed in a nuclear-weapons-free world so as to prevent rearmament. The paper then considers what political-security conditions would be required to make a nuclear-weapons ban enforceable and explores how enforcement might work in practice. Finally, it addresses the latent capability to produce nuclear weapons that would inevitably exist after abolition, and asks whether this is a barrier to disarmament, or whether it can be managed to meet the security needs of a world newly free of the bomb.