In this paper, the research progress made in the methods used for assessing the internal stability of landslide dam soils was reviewed. Influence factors such as the gradation of soil and the stress state in the soil in different analysis methods were discussed, as these can provide a reference for the development of more accurate methods to analyze the internal stability of landslide dam soils. It focuses on the evaluation of internal stability based on the characteristic particle size and fine particle content, hydraulic conditions such as the critical hydraulic gradient and critical seepage velocity, and the stress state such as lateral confinement, isotropic compression, and triaxial compression. The characteristic particle size and fine particle content are parameters commonly used to distinguish the types of seepage failure. The critical hydraulic gradient or seepage failure velocity are necessary for a further assessment of the occurrence of seepage failure. The stress state in the soil is a significant influence factor for the internal stability of natural deposited soils. Although various analysis methods are available, the applicability of each method is limited and an analysis method for complex stress states is lacking. Therefore, the further validation and development of existing methods are necessary for landslide dam soils.