In recent years, mechanisms of cooperation in power systems have attracted increasing attention from academia and industry. Such mechanisms require sharing the benefits of cooperation among participants based on some rational and obvious principles. In this regard, Cooperative Game Theory (CGT) provides a rich theoretical background for the analysis of projects where participants (called players) can make collective actions to obtain mutual benefits. CGT concepts not only solve the subsequent allocation problems but also reveal the bargaining power of players and estimate the stability of cooperation over a project. In this paper, we aim to classify and promote CGT applications in power systems. While covering a broad range of applications (such as cost and benefit allocation, transmission pricing, projects ranking, allocation of power losses), we pay particular attention to power system expansion planning. We first introduce an illustrative example of cooperation in transmission expansion planning and discuss the applicability of CGT solution concepts. To give a complete picture of the state of the art, we perform a citation network analysis of more than 3000 related studies from 1996 to 2020. Exploiting the graph layout and modularity algorithms, we identify the main research communities and highlight their contributions. We found that significant progress has been achieved in developing mechanisms of cooperation in power systems based on CGT solution concepts. However, several challenges and limitations of these concepts still have to be overcome, such as scalability, nonconvexity of cooperative games, coalitions formation assumption, ex-post game-theoretic analysis, incompleteness and manipulability of information. The overview presented in this paper and the citation network analysis performed can help scientists and engineers in comprehending the CGT solution concepts, discovering novel applications for power systems, and contributing to this promising multidisciplinary research direction.