The operation of nuclear rockets with respect both to rocket theory and to various fuels is described. The development of nuclear reactors for use in nuclear rocket systems is provided, with the Kiwi and NERVA programs highlighted. The theory of fuel element and reactor construction and operation is explained with particular reference to rocket applications. Testing sites and programs are illustrated. Future developments and applications are discussed. The conclusion that the NERVA engine is the only practical advanced propulsion system that can meet the requirements of the space transportation system in the 1980's and beyond is stated. A glossary, reading list, and motion picture list of related topics are included. (TS)