<p>Ensuring the stability and reliability of modern complex power systems with high penetration of renewable energy sources has become an increasingly critical challenge, which strongly underscores the urgent demand for robust, computationally efficient security assessment and control methodologies. In this context, synchronized ambient measurement data-driven computational methodologies have garnered rapidly growing scholarly attention, owing to their unique strengths: they enable comprehensive characterization of system dynamic behaviors under normal operating conditions, while requiring no intentional system disturbances and offering inherent operational accessibility. Existing literature has extensively explored these methodologies for modal parameters extraction for small-signal stability assessment(SSSA). The underlying computational frameworks of these approaches span advanced signal processing, system identification, and probabilistic statistical methods. Against this backdrop, this comprehensive critical review aims to provide a systematic and in-depth examination of state-of-the-art ambient data-driven computational approaches for power system security assessment. This review elaborates on the theoretical fundamentals, computational implementation frameworks, and practical engineering applications of ambient data-driven methods in tackling key challenges in modern power system security. Furthermore, it systematically summarizes the latest research advancements, identifies unresolved technical bottlenecks, and outlines promising future research directions in this rapidly evolving field. This work demonstrates the significant potential of ambient data-driven computational methodologies in enhancing the operational security and resilience of high-renewable power systems, and is intended to serve as a systematic, authoritative reference for researchers and engineers in the power system and renewable energy industry.</p>