Résumé : Elliptic curves provide an efficient public-key cryptosystem. An important tool in the study of elliptic curves is Vélu's formulas which allow to compute explicit isogenies between them. In this talk, I will explain how to generalize Vélu's formulas to abelian varieties (this is a joint work with Romain Cosset and David Lubicz). I will then describe AVIsogenies, a full open source implementation of isogeny computation between Jacobians of genus 2 curves. The interest for cryptography is that genus 2 curves allow to work over fields of half the size for the same security as with elliptic curves.