We systematically analyze a broad class of dual heterotic and F-theory models that give four-dimensional supergravity theories, and compare the geometric constraints on the two sides of the duality. In this talk I will show that F-theory gives new insight into the conditions under which heterotic vector bundles can be constructed. We show that in many cases the F-theory geometry imposes a constraint on the extent to which the gauge group can be enhanced, corresponding to limits on the way in which the heterotic bundle can decompose. We explicitly construct all dual F-theory/heterotic pairs in the class under consideration where the common twofold base surface is toric, and give both toric and non-toric examples of the general results. Finally, we provide evidence for important new aspects of G-flux in four-dimensional compactifications.