  We review a progress in obtaining the complete non-perturbative effective
action of type II string theory compactified on a Calabi-Yau manifold. This
problem is equivalent to understanding quantum corrections to the metric on the
hypermultiplet moduli space. We show how all these corrections, which include
D-brane and NS5-brane instantons, are incorporated in the framework of the
twistor approach, which provides a powerful mathematical description of
hyperkahler and quaternion-Kahler manifolds. We also present new insights on
S-duality, quantum mirror symmetry, connections to integrable models and
topological strings.
