A cohomogeneity one manifold can be thought of as a manifold which is slightly less homogeneous than a homogeneous space. More precisely, they are manifolds with an action of a compact Lie group such that the orbit space is one dimensional. Recently, Grove-Ziller constructed metrics of non-negative sectional curvature on a large class of cohomogeneity one manifolds. Cohomogeneity one manifolds are also of interest in other area of geometry and physics where they give new examples of Einstein manifolds, Einstein-Sasaki manifolds and manifolds with G_2 and Spin(7) holonomy. In this talk I will present a classification of compact simply connected cohomogeneity one manifolds in dimensions 5, 6 and 7.