Physics of cell motility J. Prost ESPCI and Curie Institute UMR168, 10 rue Vauquelin, 75231Paris cedex05, France 　　　　　Much of the cell mechanics, morphology and motility are determined by the 　　　　　dynamical properties of an actin network moving under the action of molecular 　　　　　motors and by a continuous process of polymerization/depolymerization called 　　　　　treadmilling. The actin network constitutes a physical gel the cross-links of 　　　　　which are both temporary and mobile. It is more complex than a physical gel in 　　　　　that it has a macroscopic polarity due to the microscopic polarity of actin 　　　　　filaments and in that the cross-links are dynamically redistributed by molecular 　　　　　motors. This requires an energy input, which implies that this system is 　　　　　intrinsically out of equilibrium. I will show how one can write down a set of 　　　　　phenomenological equations, which can describe this situation. I will illustrate 　　　　　the usefulness of the equations by considering several characteristic cases 　　　　　including the simple one-dimensional case, the mode structure and the 　　　　　behaviour of topological defects. I will illustrate how such developments provide 　　　　　a useful paradigm for understanding cell motility and cell dynamics. 　　　　　K. KRUSE, J.F. JOANNY, F. JULICHER, J. PROST and K. SEKIMOTO 　　　　　≪Asters, Vortices and Rotating Spirals in Active Gels of Polar Filaments≫ Phys. 　　　　　Rev. Let., 92, 078101 (2004) 　　　　　J.F. Joanny, F. Julicher, K. Kruse, J. Prost, K. Sekimoto, “Generic theory of 　　　　　active polar gels: a paradigm for cytoskeletal dynamics” to appear Eur.Phys.Jour.