Debris flow as one of the most active surface processes is an intermediate form of mass movement between mountain flood and landslide. It is a viscous and highly concentrated fluid-solid mixture, being shear-resistant like soil while flowing like water. As a typical multiphase flow, most of debris flows contain water, soil, rocks and gas, and have special inner structures. The solid grains of debris flows have very irregular shape, and their sizes range several orders of magnitude. The interactions between slurry and grain or grain and grain are complex. Therefore, it is very difficult to develop a dynamic model fully describing the debris-flow process. From the point of view of constituent prototype and motion description, the existing debris-flow dynamic models can be classified into continuum, discrete medium, and hybrid medium models. The numerical simulations based on these dynamic models are widely applied to back-analysis of debris flow discharge, predicting inundated region, risk assessment, and evaluating protection engineering etc. Comparing with the motion process of debris flow, the formation process of debris flow is an interdisciplinary research subject, and needs more attentions. Moreover, how to coupling the two processes with different spatial and temporal scales is still a challenging issue.