Abstract: The stability assessment of underground stopes is a fundamental prerequisite for safe and efficient mining operations. In this context, the Mathews stability graph method is widely adopted for open stope design as it enables the transition from qualitative geological experience to quantitative engineering evaluation. This paper systematically reviews the theoretical evolution and methodological development of the stability graph method over the past four decades through comprehensive literature analysis, comparative evaluation of representative stability graph versions, and critical examination of the mechanical significance of key controlling factors. This study focuses on the evolution of the stability number and hydraulic radius framework, and investigates the progressive refinement of rock mass quality, stress adjustment, joint orientation, gravity influence, and subsequent modification factors in different generations of stability graphs. Additionally, the historical development of major stability graph datasets and boundary calibration strategies is examined to clarify the relationships between empirical observations, engineering experience, and theoretical interpretation. The results indicate that instead of mere empirical parameter adjustment, the evolution of this method represents a fundamental advancement in understanding rock mass behavior and failure mechanisms. The modification of individual factors has gradually transformed the method from a coarse empirical design tool into a semi-mechanistic framework capable of capturing stress-path effects, structural discontinuity interactions, stress-induced brittle failure, and excavation-related damage processes. Furthermore, the controlling factors exhibit nonlinear coupling relationships associated with stress redistribution, structural complexity, and time-dependent degradation, thus indicating that stope stability is governed by multiple interacting mechanisms instead of isolated variables. Comparative assessment of different stability graph revisions demonstrates that predictive performance is improved primarily through a more realistic representation of rock mass response and failure processes instead of through statistical recalibration alone. Additionally, this review evaluates the application of statistical regression, probabilistic classification, numerical simulation, and emerging data-driven approaches in redefining stability boundaries and quantifying uncertainty. These methods improve prediction accuracy and expand the applicability of stability assessment under complex geological conditions; however, their reliability depends significantly on the database quality, sample representativeness, and regional geological characteristics. Critical challenges identified include extensive reliance on foreign empirical datasets and the limited availability of standardized local databases, which result in significant prediction errors when existing stability criteria are directly applied to fractured, weak, or highly stressed rock masses. Hence, future studies should establish localized and continuously updated stope stability databases; develop equivalent rock mass strength back-analysis methods to overcome the challenges of in-situ characterization; and integrate excavation-induced cumulative damage evolution, time-dependent deterioration, and real-time monitoring information into stability assessment frameworks. The findings indicate that advancing the stability graph method requires integrating empirical knowledge, mechanical understanding, and intelligent prediction technologies. This integration shifts stope design from static, classification-based frameworks to dynamic, adaptive, and mechanism-informed ones, thereby strengthening underground excavation stability assessment, risk management, and intelligent decision-making in modern mining engineering.