At present, high-damping rubber materials, widely used in the field of engineering seismic isolation, generally have the problems such as narrow effective damping temperature range, low damping loss factor and strong temperature dependence, which lead to prominent dependence of temperature and load conditions of the isolation performance of high-damping rubber isolation bearings. Research and development of high-performance high-damping rubber materials with broad effective damping temperature range, high damping loss factor and weak temperature dependence are very urgent and necessary to ensure the safety of the seismic isolation of engineering structures. This paper mainly reviews the recent progress in the research and development of high-damping rubber materials using nitrile butadiene rubber (NBR), epoxidized natural rubber (ENR), ethylene propylene diene rubber (EPDM), butyl rubber (IIR), chlorinated butyl rubber (CIIR), and bromine butyl rubber (BIIR). This is followed by a review of vulcanization and filler reinforcement systems for the improvement of damping and mechanical properties of high-damping rubber materials. Finally, it further reviews the constitutive models describing the hyperelasticity and viscoelasticity of rubber materials. In view of this focus, four key issues are highlighted for the development of high-performance high-damping rubber materials used for high-damping rubber isolation bearings.