A long standing problem in Riemannian Geometry is the classification of positively curved Riemannian manifolds. On the one hand there are only a few examples of such manifolds. On the other hand there is no known obstruction for simply connected closed non-negatively curved manifolds to admit a metric of positive curvature. In this talk I will discuss recent results on the classification of positively curved manifolds under mild symmetry assumptions. This is joint work with Lee Kennard and Burkhard Wilking.