Résumé
The low-energy effective action of Type II string theory compactified on a Calabi-Yau threefold is determined by the metric on the vector and hypermultiplet moduli spaces. The latter is known to receive instanton corrections coming from D-branes and NS5-branes wrapping cycles on the Calabi-Yau. I'll show how all of them can be nicely incorporated using twistorial techniques. In particular, fivebrane instantons are derived using S-duality of the type IIB formulation. I'll present also a conjecture for the Witten index of 4d N=2 gauge theories inspired by the twistorial description of the hypermultiplet moduli space.