Snow avalanches are suspensions made of snow and air belonging to the class of gravity-driven rapid mass flows. Three types of avalanches are usually considered: -Flowing (dense) avalanches have a high density ranging from 150kg/m3 to 500 kg/m3. The flow depth does not exceed 10 m but the deposit can attain 15 to 20 m for extreme avalanches. The involved snow displays various properties ranging from dry cohesion-less granular snow to highly wet snow. The mass of a flowing avalanche grows significantly as a result of snow entrainment as confirmed by recent field measurements. -Powder snow avalanches are a dilute suspension of snow particles descending slopes at very high velocities. The turbulent cloud can reach high velocities (60 to 80 m/s). The flow depth is in the range 20100 m and the density is in the range of 1-30 kg/m3. The volume of a powder avalanche grows as a result of air entrainment and their mass grows as results of snow entrainment. -Evidence from field observations confirm the existence of a density stratified flow made of two or three layers called mixed avalanches. A dense suspension is located at the bottom. A dilute turbulent suspension is located at the top. Some field observations were interpreted as the signature of an intermediate fluidized layer characterized by intermediate density and mobility compared to the dense and powder avalanches. In the presentation we will review three sets of governing equations used for modeling snow avalanches. -The depth averaged model for shallow flows is extrapolated to describe dense flowing avalanches. The friction term (Coulomb Friction) depends on the rheology of the considered material.Most models currently in use today are based on this formalism. A good knowledge of snow rheology is needed even if experiments with snow are difficult and the few available data provide only a partial knowledge of snow flows. In the presentation we will review the existing friction models and will focus on the recent results obtained on chute experiments at Col du Lac Blanc, France. To investigate the rheology of the dense flow, we carried out systematic controlled flows down a flume with natural snow. About a hundred experiments with various slope and flow discharge were performed. For each run, we measured the velocity profile, the flow height and basal stresses. The obtained data enables us to identify generic characteristics of dense snow. As a main result we pointed out the existence of two layers : a viscous upper thick layer covering a much less viscous thin layer. Additional information from discrete numerical simulation, allowed us to interpret this heterogeneity as a consequence of the snow micro structure. The lower part layer is made of single snow grains and the upper layer is made of large aggregates. Entrainment of snow by the moving avalanche is an important process to consider in such model. A review of existing model will be provided. -The KSBA model, allows a simple framework for studying the dynamics of powder-snow avalanches. In this model, the dynamics is governed by the balance between the ambient fluid entrainment from the top of the avalanche and the snow entrainment at its bottom. A recent improvement of these kind of model is the new relationship governing the ambient fluid entrainment based on the Richardson number. -The multi layers model class, considers the flow of an avalanche as a density stratified flow. The flow consists of two layers.The intermediate layer (fluidized layer) of thin depth, operates the mass and momentum exchanges between the dense and powder layers, and under certain conditions, may have its specific dynamics. Inside the dense layer, the velocity profile is highly sheared at the bottom and less sheared in the core. The friction at the base of the flow is governed by a Columbian model. Inside the powder layer, a two phase turbulent suspension of low density develops, and its flow is governed by the balance between the gravity and the turbulence of the interstitial fluid. The formation of the powder part results from the erosion by the air at the top of the moving dense part. The mass and momentum exchange are governed by conservation equations governing the intermediate layer. In the paper and the presentation, we will rapidly review the main features of these models. As conclusion, we will show that even if these models provide realistic predictions of the flow features, severals scientific bolts in the current avalanche-dynamics models persist.