The work presents a review of safety issues and assessment of potential risks associated with space nuclear power system (SNPS) operation. International and national rules and standards are considered, and accidents caused by shock impacts on SNPS are analysed. The paper demonstrates various scenarios of partial or catastrophic reactor destruction accidents caused by space launch vehicle (SLV) faults. Additionally, scenarios of space debris (SD) impact on SNPS construction are provided. The work refers to safety methods and safety provisions both managerial and constructional ones. Calculation methods for nuclear fuel final state and safety system status assessments upon accident occurrence are also developed and discussed. Prospects and potentials of future research are outlined.