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Future space power needs are extrapolated to be at least three to four orders of magnitude more than is currently available. This long-term reliable power will be required on missions such as the Space Station, Pathfinder, Space Plane, and high-powered satellites, and for national defense. Electrical insulation and dielectrics are the key electrical materials needed to support these power systems, where a single-point system failure could prove catastrophic or even fatal for the whole mission. Therefore, the impact of radiation, an environmental stress, on the properties and performance of insulation and dielectrics must be understood. The influence of radiation on polymer dielectrics, the insulating materials most commonly used for power transmission and storage, is reviewed. The effects of the type of radiation, dose, rate, and total exposure on the key electrical, mechanical, and physical properties of polymer dielectrics are described and explained.