Abstract: Driven by global climate change and intensive human activities, the hydrological cycle in the Yellow River Basin has been profoundly altered, with extreme low-flow events occurring frequently. The water crisis in the basin has evolved from a singular water quantity shortage into a complex systemic risk spanning agriculture, industry, ecology, and urban-rural water supply. Traditional approaches fall short in capturing the cross-system propagation mechanisms and nonlinear mutation characteristics of extreme low-flow risks. To address this gap, this paper first differentiates the conceptual connotations and interrelations among water crisis, hydrological drought, and water shortage, clarifying the definition of water crisis under extreme low-flow conditions. Secondly, it reveals the evolution mechanism of "natural variation initiation-anthropogenic intervention triggering – risk accumulation and mutation", and clarifies the driving mechanisms of the decline in reservoir group regulation and storage capacity, the synergistic amplification of drought in main and tributary rivers, and the imbalance of water sediment relationship on the transformation of drought into a systemic crisis. Furthermore, three types of methods including physical simulation, data-driven prediction, and complex network topology representation were sorted out, and the technical path of multi method coupling integration was demonstrated. Finally, the shortcomings of current research in fine characterization of extreme scenarios, coupling of surface groundwater processes, and resilience control were analyzed. Future directions such as joint simulation of surface water groundwater and digital twin decision support platform were proposed to provide theoretical basis for water security and risk prevention in the Yellow River Basin.