The objectives of this thesis are to investigate the theory of direct energy conversion, research the development of space nuclear power systems, evaluate the status of current systems, and draw conclusions about the feasibility and merit of using nuclear power for future space missions. Development of the earliest systems began in 1955 with the Systems for Nuclear Auxiliary Power (SNAP) Program and Project Rover. A detailed review of system design and performance is provided for the reactors and radioisotope thermoelectric generators (RTG's) of past and current programs. Thermoelectric and thermionic energy conversion techniques have been used predominantly in space nuclear power systems. The theory of these direct energy conversion methods is analyzed. Also, the safety review procedures and regulations governing the launch of nuclear sources into space are characterized. Conclusions compare accomplished levels of system performance to theoretically predicted limits and comment on the usefulness of space nuclear power for space applications.