Nuclear material nonproliferation and security issues have taken on even greater importance within the United States and internationally since the breakup of the Soviet Union in 1990s and after the terrorist attacks in the United States on September 11, 2001. Leadership in the United States has made weapons nuclear material security and nuclear material elimination and/or reduction a high national priority. For future National Aeronautics and Space Administration (NASA) missions, the use of highly enriched uranium (HEU) in space nuclear reactors and propulsion systems may be enabling for certain missions, and therefore, it is important that it remain an available option within the context of U.S. nonproliferation policy. This critical review provides an overview of U.S. nonproliferation policy on the use of HEU in nuclear reactor systems for the three primary users of HEU: U.S. Navy, domestic and international civilian research and test reactors, and future NASA missions. In general, U.S. nonproliferation policy is based on a risk versus benefits approach. Nuclear security is a key aspect of nuclear nonproliferation and within the field of space nuclear reactors. Nuclear security requirements and implementation procedures are well established for all phases of nuclear design, manufacturing, transportation, and testing programs. The only time that nuclear material may be outside of direct physical control and security would be during operation in deep space or a planetary surface mission or due to an accidental reentry of a space nuclear reactor during launch or postoperation from low earth orbit. Safety and security options for accidental low-probability reentry events are discussed.