Résumé
I'll review the recent progress in understanding of non-perturbative effects in Calabi-Yau compactifications of type II string theories. I'll show that combining non-perturbative symmetries and dualities of string theory with a geometric framework based on certain twistor spaces, it is possible to find all D-brane instanton corrections to the hypermultiplet moduli space of compactified string theory. These corrections are encoded in a simple dilogarithm function and have a nice geometric description. Besides, this approach allows also to obtain a non-perturbative generalization of the classical mirror map and has various relations to other aspects of stringy non-perturbative physics.