I review my recent work on how to do exact computations for certain D-branes on Calabi-Yau spaces. The methods developed to date cover mostly only non-generic situations (non-compact geometries, non-intersecting branes). Despite the set of possible correlation functions is infinitely richer for intersecting branes, very little work has been done so far in physics. The underlying mathematical framework is homological mirror symmetry. This heavy machinery is quite abstract and has not been developed as far such as to allow for an explicit computation of physical quantities. Our approach is based on a concrete field theoretical realization in terms of matrix factorizations, which does allow for explict computations, eg. of exact superpotentials.