Understanding rock failure behaviors is crucial for various engineering applications, including geotechnical engineering, mining, petroleum engineering, and underground construction. Rock failure criteria provide essential tools for the prediction of mechanical response of rocks under different loading conditions. This review article overviews various rock failure criteria, highlighting their underlying theories, modeling approaches, and applications. The paper discusses classical failure criteria and extended criteria based on them, such as Mohr-Coulomb (M−C), Hoek-Brown (H-B), and Griffith Criteria, as well as more advanced criteria incorporating rock fabric, anisotropy, and complex failure modes. The review also explores machine learning approaches for rock failure prediction and uniaxial compressive strength based on experimental and real-time well-log data to determine and validate rock failure criteria. The insights provided in this article can assist researchers, engineers, and practitioners in selecting appropriate failure criteria for specific rock types and engineering projects. Rock failure criteria are crucial in mining for evaluating stability, optimizing operations, and ensuring safety.