The interaction between the catenary and pantograph is one of the most crucial factors that determine the train operation in high-speed railway. The bad state of catenary is able to directly influence the power supply safety of traction power system. In this paper, four aspects on the catenary research of high-speed railway are reviewed in detail, namely the solution methods for catenary equilibrium state, the dynamic modeling methods of catenary, non-contact detection methods of catenary, and the static and dynamic evaluation methods of catenary. In addition, their recent advances are described. For the low solution accuracy of the initial equilibrium state of catenary, the structure finding method with multi-objective constraint and nonlinear finite element procedure are introduced to solve the problem. For the catenary’s dynamic modeling, considering the influence of environmental wind on the catenary, environmental wind simulations and wind tunnel tests are used to obtain the aerodynamic coefficients and build the wind field along the catenary for analysis of its wind vibration characteristics. In order to improve the detection accuracy of non-contact detection for the catenary, the deep learning theory and real-time detection algorithms should be adopted in the future. In view of the lack of dynamic assessment method for the catenary, the modern spectrum evaluation, time–frequency analysis, big data technology and their combinations will be the important means for future catenary evaluation.