Abstract: Insulation systems composed of cooling media and polymers are widely used in the fields of superconductivity, space environment simulation, biomedicine, and nuclear fusion. However, discharge failure problems often occur on cooling media, polymer materials, and their interfaces. Due to high test cost, long cycle, lack of instruments, safety risk, and other adverse factors at cryogenic temperature range, the research on discharge test, discharge rule, existing theory verification, and new theory proposal is far from enough. Therefore, the experimental results and theoretical progress of dielectric breakdown and flashover at cryogenic temperature range were reviewed in this paper. The summary of the laws and the analysis of discharge characteristics were also emphasized. Furthermore, the existing mechanisms were commented and work schemes for the future were proposed. In particular, the multiple influences of aging factors on dielectric breakdown were analyzed; the research of solid-liquid, gas-solid interface discharge behavior, and the limitations of existing models were expounded; the transport mechanism of space charge and its application scope in the cryogenic range were also discussed; the measurement methods and results of charge and trap at cryogenic temperature range were summarized at last. The research was helpful to promote the development of insulation theory at cryogenic temperature range, and was beneficial to solve the engineering problems. It also provided plenty references for the design and optimization of low-temperature insulation structure, material selection, and new material research and development.