During this century, humankind must deal with increasing demand for energy and the growing impact of burning fossil fuels. Nuclear power, which presently produces 14% of global electricity, is a low-carbon-emissions alternative. However, the sustainability of nuclear power depends on the amounts of uranium and thorium available, the economics of their recovery from ore deposits, and the safety and security of nuclear materials. Unlike combustion of hydrocarbons, which determines the amount of fuel needed for a given amount of energy, nuclear reactions can create additional fissile isotopes. Hence, the choice of nuclear fuel cycle profoundly affects the size of the nuclear resource, as well as nuclear waste management and the risk of proliferation of nuclear weapons. We argue that uranium resources, identified and yet to be discovered, could sustain increases in nuclear power generation by a factor of two or three through the end of this century, even without advanced closed-fuel-cycle technologies.