A long standing open problem in Riemannian Geometry is the classification of positively curved manifolds. So far it has been a successful approach to consider the classification problem under the assumption of large symmetry, i.e. under the assumption that the isometry group is large in some sense. In this talk I will report on ongoing joint work with Lee Kennard and Burkhard Wilking in which we consider positively curved manifolds with relatively small isometry group.