Delay/Disruption Tolerant Networks (DTNs), which are based on an overlay protocol and the store-carry-forward paradigm, are considered as a promising solution to cope with the challenges imposed by space environment, such as long delay, intermittent connectivity, etc. Contact Graph Routing (CGR) is a dynamic routing algorithm which can compute routes by taking advantage of a priori knowledge of the space DTN topology. In this paper, the basic principles and algorithm procedures of the CGR are introduced, and the definitions of the associated terminologies and corresponding formulas are given, firstly. Then, the existing enhancements of the CGR are summarized in terms of routing loops avoidance, computational efficiency, routing accuracy, congestion control, opportunistic extension, and exception handling. Next, the representative real test experiments that have been conducted to evaluate the applicability of the DTN protocol stack and CGR, are outlined, and the performance differences between the CGR algorithm and the multi-layered satellite routing algorithm (MLSR) are evaluated by GEO/MEO/LEO satellite network simulation. Finally, the future developments of CGR are given, including the integration of CGR-extension block (CGR-EB) and cache-CGR (C-CGR), opportunistic CGR, CGR extension to large network, CGR-Quality of service (QoS) provision, enhancement of contact plan description method, etc.