The seminal theorem of Cheeger and Gromoll characterizes open manifolds of non-negative sectional curvature by showing that any such manifold, $M^n$, is diffeomorphic to the normal bundle of a totally convex, closed submanifold $\Sigma^k$, a \textit{soul} of $M$. This brings up a far-reaching open problem: given a closed manifold $\Sigma^k$ with non-negative sectional curvature, which vector bundles over $\Sigma$ admit complete metrics with non-negative curvature? In this talk we will talk about the history of this problem and answer a longstanding question of Grove-Ziller. We show that every vector bundle over every homotopy 7-sphere admits non-negative curvature. This is joint work with David Duncan and Rebecca Field.