Thanks to Gromov's pre-compactness theorem and the work of Cheeger and Colding, any complete n-manifold with nonnegative Ricci curvature and Euclidean volume growth is asymptotic to a family of cones at infinity in the pointed Gromov-Hausdorff sense. When n=4, a naive argument suggests that the sections of these cones are positively Ricci curved and hence homeomorphic to spherical space forms by Hamilton's work. I will discuss joint work with Elia Bruè and Alessandro Pigati where we make this argument rigorous.