Abstract: CP violation in non-leptonic B decays allows to extract the phases of the CKM matrix describing flavor mixing in the quark sector. Obtaining these weak phases from the experimental data is hindered by the presence of non-perturbative strong interaction dynamics, which can not be calculated from first principles in QCD. In this talk I will show how Soft Collinear Effective Theory allows to isolate the non-perturbative effects into a few universal matrix elements, which can be determined from data itself. This allows a determination of the weak angle gamma with very small theoretical uncertainties.