Hydraulic failure in levees, river embankments, and earth dams represents a critical challenge in flood risk management, particularly under increasing climate-induced hydrological stresses. This study presents a systematic literature review of numerical, probabilistic, and data-driven modeling approaches used to assess hydraulic failure mechanisms in earthen flood-protection structures. A structured search was conducted in Scopus, Web of Science, and Taylor & Francis for peer-reviewed English-language journal articles published between 2015 and 2026. Following duplicate removal, title and abstract screening, and full-text eligibility assessment, 65 studies were included in the final synthesis. Based on the synthesis, an integrated mechanism–model–uncertainty framework is developed to relate hydraulic loading conditions, soil response, dominant failure mechanisms, appropriate numerical modeling approaches, uncertainty treatment, and climate-related stressors. This study provides valuable insights for engineers, researchers, and policymakers by identifying key advances, limitations, and future research directions for improving levee resilience. Study quality was assessed using a structured quality assessment rubric. The review protocol was not registered in a public registry, and no external funding was received.