This review provides a concise overview and summary of the research findings and recent advancements by scholars worldwide on the migration mechanisms of gases, experimental methods for gas migration, gas migration characteristics influenced by various factors, and gas migration models within high-level radioactive waste geological repositories. The study indicates that during the operation of deep geological repositories, gases migrate in buffer/backfill materials primarily through three mechanisms: pure diffusion, gas–water two-phase flow, and gas breakthrough, which can be characterized by different types of gas migration models. Common experimental techniques in gas migration research include the transient diffusion method, controlled gas injection rate method, and pressure control method, among others. Extensive gas migration test results demonstrate that the gas migration characteristics in buffer/backfill materials are mainly influenced by their physical properties (such as dry density, saturation, porosity, sand content, etc.) and boundary conditions (such as confinement, mechanical state, and temperature, etc.). Given the complexity of actual operating conditions in high-level radioactive waste geological repositories, a priority for future research should be the development of advanced instrumentation to investigate the gas migration characteristics of buffer/backfill materials under multi-field (thermal-hydro-chemical–mechanical) and multi-phase (solid–liquid-gas) coupling conditions, elucidate mechanisms, establish models, and conduct numerical simulations, marking it as a significant research direction for the future.