I will present recent progress in computing non-perturbatively exact superpotentials of certain N=1 supersymmetric string compactifications. The efficient and systematic method relies on a non-trivial generalization of mirror symmmetry to Calabi-Yau manifolds with D-branes on top of them. The approach puts the computation of N=1 superpotentials W on a footing similar to the familiar computation of the prepotential F in N=2 theories; the main new physical ingredient is
that besides the usual closed string instantons, also disk instantons from the open string sector contribute. The whole framework may be viewed as the N=1 counterpart of the well-known N=2 'special geometry'.
