Selective maintenance is regarded as a type of profit-generating maintenance policy, playing an important role in balancing limited maintenance resources with system performance. Since 1988, increasing interest has been focused on this research area. Nevertheless, to the best of our knowledge, there is a lack of critical reviews of selective maintenance. This paper is the first systematic review focusing on this relevant topic. In this work, a definition and some specific features of selective maintenance are elaborated. Based on these features, a set of criteria that have been considered in selective maintenance optimization are summarized into 3 categories: system characteristics, maintenance characteristics, and mission profile characteristics. Based on these criteria, a comprehensive literature review on selective maintenance is undertaken. The solution approaches, as well as a general procedure for selective maintenance optimization, are discussed. Finally, some possible directions for further research are provided.