Given the frequent occurrence of landslide-induced river blockages in the alpine and canyon regions of southwestern China and based on the physical process of landslide-induced river blockage, this paper systematically reviews the research progress of continuum mechanics methods, discontinuum mechanics methods, and coupling methods in simulating landslide-induced river blockage processes, with a focus on analyzing the advantages and limitations of these methods in terms of computational accuracy, computational efficiency, and scope of application. The application of these methods in typical engineering cases is also discussed. Furthermore, the paper summarizes current key technical challenges in numerical simulation of landslide-induced river blockage processes, including high-performance computing, multi-scale modeling, parameter uncertainty handling, and coupling stability issues. Finally, future research directions are proposed, such as leveraging high-performance computing platforms, developing multi-scale coupled modeling techniques, advancing intelligent parameter inversion, and enhancing uncertainty quantification.