A review is given of the present state of work on the development of satellite solar power stations (SSPS) that will be placed in geosynchronous orbits and will convert solar into electric energy and then transfer it in the form of a microwave beam to the earth's surface. The idea of the SSPS was first put forward in 1968 and has since been the subject of considerable development work by a number of companies and government agencies in the USA. SSPS may be regarded as a promising variant of a power system that is capable, at least in principle, of solving the basic problem in power engineering since it is capable of drawing upon an inexhaustible source of energy (the sun). It is also capable of eliminating the problem of ecological contamination, of high efficiency of the energy transfer system (up to 80\%), and of flexibility in the redistribution of the available energy among remote consumers. The review analyzes the individual aspects of the problem of developing the SSPS.