The kinetic approach to conservation laws concerns various aspects of the theory of hyperbolic systems. For those with a rich enough family of entropies, it allows to give a kinetic formulation which is a way to represent by a single equation the whole family of entropies. For scalar conservation laws it turns out to be a powerful tool to understand their mathematical structure and unify in a simple formalism most of the theory. As an example remains the proof of Sobolev regularizing effects for nondegenerate fluxes in multidimensional scalar conservation laws. Many open theoretic questions are still open which will be mentioned during the talk.

More general, and useful for applications, is the derivation of stable numerical schemes for systems of gas dynamics type. As an example, we will explain how the kinetic schemes furnish a natural answer to the question of deriving numerical methods which preserv equilibriums for the Saint-Venant model of shallow water.

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