In this thesis, novel corrections to B → X˦ and B → Xl+l- decays, where X is a pseudoscalar or vector meson, are presented. These are the chromomagnetic matrix element, weak annihilation in a general four-quark operator basis and a long-distance charm loop contribution. The calculation of the chromomagnetic matrix element completes the calculation of matrix elements for all relevant effective weak operators in B → V decays, removing an infrared divergence which previous computations had treated in a very approximate way. It also encounters an interesting technical obstacle not previously seen in sum rule calculations, which is likely to be encountered regularly in future once higher order loop diagrams are calculated. The potential for this term to contribute to the CP asymmetry in D → V˦ in the presence of new physics is discussed. The improved computation of weak annihilation diagrams is applied to the analysis of isospin asymmetries in radiative and semi-leptonic B → (p;K(*)) decays, and the computation of long distance charm bubble terms is applied to produce an improved prediction for time-dependent CP asymmetries in various B → V decays.
