As opposed to the string coupling, F-theory has a perturbative formulation in terms of the string length. Computing $alpha^prime$ corrections to the F-theory effective physics is a challenging task and is of great relevance in string phenomenology. In this talk, I will present a modest progress in this program. par Firstly, I will be focusing on F-theory compactified on K3xK3 and discuss the exact Kaehler potential in the $alpha^prime$ perturbation theory for the vector multiplets of the ensuing 4d, N=2 effective theory. The various (non)-perturbative dualities which this specific model features greatly simplify the analysis and makes manifest the SL(2,Z)-invariant structure of the quantum corrections. Secondly, I will discuss general 4d, N=1 F-theory compactifications. Using the M/F-theory duality I will derive a novel, genuinely N=1 string correction to the internal volume and discuss its properties. \ \ The talk is based on the following papers: arXiv:1212.4831 and arXiv:1303.3317.