The stages (1970–2018), forecasts and prospects for development of the nuclear power industry in the world, in Russia and in other countries (2019–2050) are considered. The issues of nuclear fuel supply are analyzed. The paper presents an overview of construction and grid connection of nuclear power plants in the world in 1954–2018. We have given a classification for accidents at nuclear power plants and their impact on development of the nuclear industry is assessed. We have considered the dynamics of electricity generation at nuclear power units in 1970–2018, analyzing the explored and recoverable reserves, production volumes and the demand for natural uranium. We have composed a forecast for projected growth in total installed capacity of nuclear power units in the world up to 2050, a forecast for growth in global electricity generation at nuclear power plants, as well as forecasts for growth in global consumption of uranium and its proven reserves in 2016–2050.