The low-energy effective action of compactified Type II string theory is determined by the geometry of its moduli space which receives instanton corrections. I'll present a non-perturbative description of this moduli space, which crucially relies on the twistor approach to quaternionic geometries. Using this approach, I'll show how one can incorporate contributions from all D-brane instantons and give some partial results on instanton effects generated by NS5-brane. I'll argue that, ignoring the latter contributions, the moduli space corresponds to an integrable system.