The pronounced aero-hydrodynamic coupling effects of modern Wind-Assisted Propulsion System (WAPS) ships challenge the applicability of traditional stability frameworks, which are predicated on hydrostatic energy balance, in satisfying the dynamic constraints of the Second Generation Intact Stability Criteria (SGISC). This paper systematically reviews the methodological evolution of dynamic stability assessments for WAPS ships under extreme and damaged conditions. By introducing a "Hierarchy of Evidence" evaluation framework, this study delineates the applicability boundaries of aerodynamic Reduced-Order Models (ROM), extended 3/4-DOF maneuvering equations, and 6-DOF time-domain hybrid architectures, defining the role of high-fidelity CFD-VPP in establishing calibration benchmarks. The review also discusses the damping distortion mechanisms induced by multiphase flow sloshing under damaged conditions. Synthesized findings indicate that transitioning towards a 6-DOF time-domain coupled architecture provides clear advantages for capturing unsteady aerodynamic hysteresis and nonlinear interference. Meanwhile, surrogate models, such as Physics-Informed Neural Networks (PINNs), offer a potential pathway to mitigate the computational demands associated with long-term extreme value extrapolations. Ultimately, this review provides a methodological reference for the high-fidelity assessment of WAPS and the development of Digital Twin systems.