In this talk we will start by briefly describing the classification of compact simply connected cohomogeneity one manifolds in low dimensions. A powerful result of Grove-Ziller allows us to put metrics of nonnegative sectional curvature on many of these manifolds and elementary methods allow us to construct such metrics on many others. After this there is only one family of manifolds left which are previously not known to admit metrics on nonnegative sectional curvature. We will describe a method of constructing nonnegatively curved metrics on these spaces, thus completely settling the question of which compact simply connected cohomogeneity one manifolds in dimensions 7 or less admit invariant metrics of nonnegative sectional curvature