This review summarizes the mechanisms, experimental methods, and breakthrough models concerning gas breakthrough in buffer and backfill materials within high-level radioactive waste repositories. It analyzes the characteristics of gas breakthroughs influenced by various factors and presents recent research progress and findings in this area. Research findings indicate that activities such as metal corrosion within disposal repositories yield a variety of gases, leading to the accumulation of gas pressure. Commonly used experimental techniques in gas breakthrough studies include incremental pressurization, mercury intrusion porosimetry, and residual capillary pressure measurement. Extensive gas injection experiments demonstrate that the breakthrough pressure of buffer/backfill materials is influenced by factors such as confining pressure, boundary conditions, material properties, temperature, and saturation. Gas breakthrough mechanisms are categorized into capillary, mechanical, and interfacial types, forming the basis for various breakthrough models. Given the complex operational conditions in disposal repositories and the limitations of experimental tools, future research should prioritize developing instrumentation to investigate gas breakthrough in buffer/backfill materials under multi-field (thermal-hydro-chemical-mechanical) coupling conditions, elucidating mechanisms, establishing models, and conducting numerical simulations.