Safe disposal of high-level radioactive nuclear waste (HLW) is crucial for human health and the environment, as well as for sustainable development. Deep geological disposal in sparsely fractured crystalline rock is considered one of the most favorable methods for final disposal of HLW. Extensive research has been conducted worldwide and many countries have initiated their own national development programs for deep geological disposal. Significant advancements of national programs for deep geological disposal of HLW in crystalline rock have been achieved in Sweden and Finland, which are currently under site development stage, focusing on detailed site characterization, repository construction, and post-closure safety analysis. Continued research and development remain important in the site development stage to ensure long-term safety of the HLW disposal repository. This work presents an overview and discussion of the progress as well as remaining open scientific issues and possibilities related to site development for safe disposal of HLW in crystalline rock. We emphasize that developing a comprehensive and convergent understanding of the coupled thermal, hydraulic, mechanical, chemical and biological (THMCB) processes in fractured crystalline rock remains the most important yet challenging topic for future studies towards safe disposal of HLW in crystalline rock. Advancements in laboratory facilities/techniques and computational models, as well as available comprehensive field data from site developments, provide new opportunities to enhance our understanding of the coupled processes and thereby repository design for safe geological disposal of HLW in crystalline rock.