Landslide dam is one of the main types of barrier dams, whose structure is loose and stability is poor. Once seepage failure occurs, it will threaten the life and property safety of downstream people. The particle composition and depositing characteristics of the dam are key influence factors in evaluating the seepage safety of landslide dams, which are also the primary considerations to carry out model tests. Based on previous studies, combined with the results of field investigations and indoor model tests, the depositing characteristics of landslide dams and advances in model tests for seepage failure are summarized, and the existing problems are discussed. Results show that the depositing characteristics of the landslide dam are related to the lithology of landslides, sliding path, bank slope structure, etc. The failure modes and processes of landslide dams are varied from depositing characteristics, particle size compositions to hydraulic conditions. For the landslide dams with high permeability zones, their failure can be attributed to the progressive cycle of piping and downstream dam slope collapse. While designing a model test, experimenters should not only consider the dynamic flow similarity but also determine the particle size distribution of the dam soils according to the relationship between particle size and particle movement. Finally, it is proved that the grading entropy can comprehensively reflect the gradation characteristics of the landslide dam as well as the change in gradation in the fine particle erosion process, which can be used to predict the permeability and internal stability of dam particles. Combined with other information, the failure mode and process of landslide dam can be predicted. The research results can provide references for the experimental research of landslide dam.