Flexural toppling is typically observed in anti-dip bedding rock slopes with a set of steeply dipping parallel joints against the slope face. This failure occurs due to the bending of rock strata, similar to cantilever beams. However, the exact failure surface is usually unknown, which leads to an assumption regarding the location and shape of the failure surface that must be made in the theoretical analysis. This assumption serves as the basis for stability analysis but may lead to errors if it is not appropriate. Therefore, in this study, we provide a detailed and systematic review of the mechanical model, precondition, failure patterns of rock strata, primary controlling factors, morphological characteristics of slope failure surfaces, and theoretical analysis methods of slope stability. We also introduce two practical application cases to better understand the advantages, disadvantages, and application scope of these methods. Additionally, we discuss the existing issues and potential future research developments in this field. [ABSTRACT FROM AUTHOR]