The lithium–sulfur battery is considered as one of the most promising next-generation energy storage systems owing to its high theoretical capacity and energy density. However, the shuttle effect in lithium–sulfur battery leads to the problems of low sulfur utilization, poor cyclability, and rate capability, which has attracted the attention of a large number of researchers in the recent years. Among them, the catalysts with efficient catalytic function for lithium polysulfides (LPSs) can effectively inhibit the shuttle effect. This review outlines the progress of catalyst materials for lithium–sulfur battery in recent years. Based on the structure and properties of the reported catalysts, the development of the reported catalyst materials for LPSs was divided into three generations. We can find that the design of highly efficient catalytic materials needs to consider not only strong chemical adsorption on polysulfides, but also good conductivity, catalysis, and mass transfer. Finally, the perspectives and outlook of reasonable design of catalyst materials for high performance lithium–sulfur battery are put forward. Catalytic materials with high conductivity and both lipophilic and thiophile sites will become the next-generation catalytic materials, such as heterosingle atom catalysis and heterometal carbide. The development of these catalytic materials will help catalyze LPSs more efficiently and improve the reaction kinetics, thus providing guarantee for lithium sulfur batteries with high load or rapid charge and discharge, which will promote the practical application of lithium–sulfur battery.