In this talk I'll explore the new results in the underlying geometry of dual heterotic/F-theory compactifications. I will describe a systematic analysis of 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. I will demonstrate that F-theory gives new insight into the conditions under which heterotic vector bundles can be constructed. Finally, I describe new results on the structure of the dual 4-dimensional N=1 effective theories, including global/geometric interpretations of interesting open-string data, such as so-called ’T-brane’ solutions corresponding to nilpotent Higgs fields in a 7-brane world sheet theory.