Résumé
I'll review the current understanding of the low energy effective theory resulting from compactifications of Type II superstrings on Calabi-Yau manifolds. The effective action can be encoded into the metric on a moduli space which is known to receive quantum stringy corrections, both perturbative and non-perturbative. The description of instanton effects crucially relies on twistorial methods and points toward a deep relation to integrable structures.