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Abstract. We obtain a dichotomy for C1-generic, volume preserving diffeo-morphisms: either all the Lyapunov exponents of almost every point vanish or the volume is ergodic and non-uniformly Anosov (i.e. hyperbolic and the splitting into stable and unstable spaces is dominated). We take this dichotomy as a starting point to prove a C1 version of a conjecture by Pugh and Shub: among partially hyperbolic volume-preserving Cr diffeomorphisms, r> 1, the stably ergodic ones are C1-dense. To establish these results, we develop new perturbation tools for the C1 topology: “orbitwise ” removal of vanishing Lyapunov exponents, linearization of horseshoes while preserving entropy, and creation of “superblenders ” fro