This PhD thesis deals with two examples of the dualities relating the five known superstring theories and eleven dimensional supergravity. The dualities allow to gain insight into certain aspects of the non perturbative behaviour of string theory. In the first part, type IIA string theory compactified on a complex four dimensional Calabi-Yau manifold is considered. Switching on non trivial background fields from the Ramond-Ramond sector introduces a potential in the low energy effective action. This potential receives infinitely many corrections due to world sheet instantons. For the case of a threefold fibred over a large P1 base, these corrections could be derived in this thesis using mirror symmetry. The second part of the thesis considers the duality between the strongly coupled E8 × E8 heterotic string and eleven dimensional supergravity compactified on an interval. Both theories are compactified further to six dimensions on a four dimensional orbifold. Anomaly cancellation conditions fix both the spectrum and the gauge group. To gain a deeper understanding of the somewhat surprising rules for spectrum and gauge group, the dual six dimensional F-theory formulation is constructed in the thesis. The geometry of the six dimensional F-theory compactification manifold indeed gives an explanation of the non-perturbative gauge group.