Abstract: Large-scale space structures (LSSS), such as giant space solar power stations and long-baseline space-based optical instruments, hold significant application value; however, their on-orbit construction and maintenance represent formidable challenges in the aerospace field. As a key enabling technology for the high-efficiency and low-cost implementation of these tasks, LSSS climbing robots offer distinct advantages by operating without propellant consumption while covering extensive workspaces. This paper reviews and summarizes recent research on space structure climbing robots, exploring the key technologies, core challenges, and future directions in this field. To this end, the paper first introduces representative design schemes and the development progress of principle prototypes from both domestic and international efforts, viewed from an overall technology perspective. Subsequently, it provides a comparison of the advantages and disadvantages of typical adhesion technologies and locomotion modes, and discusses the design for adaptability to the space environment from the perspective of enhancing the robot's in-service reliability. In addition, focusing on various climbing robot design schemes, this paper analyzes the current status and limitations of research in gait and motion planning. It also discusses the challenges and progress in the dynamics modeling and motion control of space climbing robots. Finally, based on a discussion of the relevant scientific problems and key technical difficulties, this paper provides an outlook on several future research directions worthy of attention.