A 2-connected, rational homotopy 7-spheres is classified up to diffeomorphism by three invariants: its (finite) 4th cohomology group, its q-invariant and its Eells-Kuiper invariant. The q-invariant is a quadratic refinement of the linking form and determines the homeomorphism type, while the Eells-Kuiper invariant then pins down the diffeomorphism type. In this talk, I will discuss the diffeomorphism classification of a certain family of non-negatively curved, 2-connected, rational homotopy 7-spheres, discovered by Sebastian Goette, Krishnan Shankar and myself, which contains, in particular, all S^3-bundles over S^4 and all exotic 7-spheres.