As our societies become more and more risk averse, the risk levels of the early expedition missions are no longer tolerable. Risk management in the space sector is rapidly growing to cope with increasing risks coming out of more advanced and complex systems. In this paper, the necessity of the use of risk management methods is illustrated through an analysis of the evolution of mission failures over the years coupled with a literature overview of the state-of-the-art tools focusing on mission classification frameworks. A bibliometric analysis is also performed with the aid of the VOSviewer software on a corpus of 6375 scientific documents extracted from the SCOPUS database. Six clusters of risk parameters are identified: a) dependability and reliability, b) cost and criticality to the agency, c) complexity, d) manned space missions, e) mission objectives and f) space hazards. The results show that two of the parameters, previously omitted in the mission classification frameworks of NASA and ESA, manned space missions and space hazards, should be included in the set of a mission’s risk parameters. Finally, the paper concludes with a geographical and research fields’ distribution analysis of the available publications.