Debris flow is a kind of mass movement of viscous and highly concentrated fluid-solid mixture between hyper-concentration flow and landslide. It has both solid and liquidity properties, being shear-resistant like soil while flowing like a fluid. The existing debris-flow dynamic models, most of which originate from hydraulic or geotechnical models, can be classified into three types： continuum, discrete medium, and hybrid medium models with respect to constituent prototype and motion description. The former two are able to explain some phenomena related with debris flows to some extent. Traditional single-fluid and multi-fluid models are belong to the continuum model. The discrete medium model contains DEM （discrete element model） and kinetic model. The hybrid model is able to describe debris-flow features completely, but has more theoretical and computational problems than the other two. A debris-flow numerical model is composed of dynamic model, numerical scheme, computational trick, and handling of boundary and initial conditions. The important factors that strongly influence the simulation result in the numerical model include numerical algorithm,  rheological model,  topography data,  temporal and spatial resolutions etc. The trend in this field is to model the full process of debris flow, develop non-homogeneous computational model, take the effect of big boulder into account, and consider the mass exchange between the flow and bed.