Abstract: A Markov jump linear system (MJLS) is a random system with multiple modes. The jump transition of the system between each mode is determined by a set of Markov chains. The MJLS model can accurately describe the system in actual engineering applications because it can produce mutations in the representation process. In recent years, the optimal control problem of the MJLS has become a research hotspot. Dynamic programming, maximum value principle, and linear matrix inequality have become the mainstream methods to solve such problems. This paper reviews the current research status of the MJLS optimal control field. The research status of MLJS optimal control problems at home and abroad under general conditions, noise conditions, time delay conditions, and some specific conditions are discussed individually. Finally, the research direction of the MJLS optimal control field worthy of attention in the future is summarized and put forward.