F-theory can be thought of the correct way to describe Type IIB theory with 7-branes in generic situations where the string coupling cannot be assumed to be small. It geometrizes the variation of the string coupling and the backreaction of the 7-branes on the ambient space by introducing two additional auxiliary dimensions. Thus, it is formulated using twelve dimensions. For string phenomenology it is very interesting because one the one hand exceptional gauge groups are available, which are highly relevant in the context of unification and are heavily exploited in heterotic string theory, and on the other hand the particle physics degrees of freedom localize on submanifolds of the compactification, as is the case in Type II theories with intersecting D-branes. Given this localization, a considerable number of phenomenological questions can be answered in a so-called local model where large parts of the compactification space are decoupled and particle physics essentially takes place in eight space-time dimensions. I will briefly introduce the mathematical description of the theory and then focus on local model building with explicit examples in the framework of SU(5) GUTs.