In this talk I will summarize joint work with Wolfgang Ziller. In contrast to the positive curvature setting, there exist comparatively many examples with non-negative sectional curvature. Hence it is natural to ask whether, among the known examples, it is possible to topologically distinguish manifolds with non-negative curvature from those admitting positive curvature. We study the topology of various sphere bundles over CP^2 which admit a metric of non-negative sectional curvature. We then compare their diffeomorphism types with known examples of positively curved manifolds. I will also discuss a recent simplification of the homeomorphism invariants of such manifolds obtained jointly with Pongdate Montagantirud.