Let X be a closed smooth manifold endowed with a smooth volume. A volume preserving diffeomorphism f of X is called ergodic if any f-invariant measurable set is either of full measure or of measure zero. A volume preserving diffeomorphisms f is called stably ergodic if there is a neighborhood of f in C^r-topology consisting only of ergodic diffeomorphisms. Classical results of Kolmogorov, Arnold and Moser show that stable ergodicity is not always a generic property in the class of C^r volume preserving diffeomorphisms. In contrast, Anosov showed that a volume preserving uniformly hyperbolic diffeomorphisms is stably ergodic. Later, Grayson, Pugh, and Shub, found the first example of a non-hyperbolic stably ergodic diffeomorphism, the time-1 map of the geodesic flow of a surface of constant negative curvature. It was conjectured by Pugh and Shub that the set of stably ergodic diffeomorphisms is open and dense among the partially hyperbolic C^2 volume preserving diffeomorphisms of a compact manifold. During my talk I shall show evidence for a positive answer to the latter conjecture, and present new examples of stably ergodic diffeomorphisms.