I will report on recent joint work with Andrey Gogolev on Anosov bundles. These are smooth fiber bundles M --> E --> X whose fibers are equipped with either an Anosov diffeomorhism or an Anosov flow. (Here the fiber M is a closed smooth manifold and the structure group is Diff(M).) We give examples of non-trivial bundles which are Anosov and also show, under quite general conditions, that Anosov bundles are topologically trivial. One application is to shed light on the following: Conjecture (Farrell-Ontaneda). Every negatively curved bundle with simply connected base space is topologically trivial. A negatively curved bundle is one where each fber is equipped with a negatively curved Riemannian metric.