Abstract: Intact stability of ships in waves is a core guarantee for navigation safety. The direct stability assessment method of the Second Generation Intact Stability Criteria (SGISC) remains immature, becoming a current research focus. This study aims to systematically review the research progress and key issues of direct stability assessment for SGISC worldwide. Methodologically, it focuses on summarizing the numerical prediction technologies (including potential flow methods, viscous flow methods, hybrid viscous-potential flow algorithms, and intelligent computational methods) for five stability failure modes: parametric rolling, pure loss of stability, surf-riding/broaching, excessive acceleration, and dead ship stability. Additionally, three categories of statistical extrapolation methods addressing the rarity of stability failures are analyzed in depth, namely extreme value theory approaches, critical wave groups and wave episode methods, and environmental condition extrapolation methods. The results show that potential flow and viscous flow methods have achieved remarkable results in predicting most failure modes, while intelligent methods and hybrid viscous-potential flow algorithms demonstrate application potential. However, several key issues remain unresolved, such as the high dependence of intelligent methods on high-quality data, insufficient simulation accuracy of multi-degree-of-freedom coupling for pure loss of stability and surf-riding/broaching, the need for improved propeller-rudder emergence models, and excessive computational cost of full viscous flow simulations. In conclusion, future research directions are proposed, including strengthening experimental data validation, optimizing the combination of viscous flow methods with extrapolation techniques, exploring the applicability of different extrapolation methods for various failure modes, conducting more sample ship calculations, and standardizing databases for intelligent methods. This study provides a reference for the engineering application of direct stability assessment technology in SGISC.