The safe disposal of high level radioactive waste is a challenging task facing the scientific，technological and engineering communities. This paper reviews the latest progress of high level radioactive waste disposal programs，with focus on the progress in underground research laboratories, including the following key scientific issues: the precise prediction of the evolution of a repository site, the characteristics of deep geological environment, the behaviour of deep rock mass, groundwater and engineering materials under coupled conditions (intermediate to high temperature, geostress, hydraulic, chemical, biological and radiation process), the geochemical behaviour of transuranic radionuclides with low concentration and their migration with groundwater, and the safety assessment of the disposal system.