  This thesis examines the non-leptonic B-decays within QCD factorisation and
beyond, to challenge the assumptions and limitations of the method. We analyse
the treatment of the distribution amplitudes of light mesons and present a new
model described by simple physical parameters. The leading twist distribution
amplitudes of light mesons describe the leading non-perturbative hadronic
contributions to exclusive QCD reactions at large energy transfer, for instance
electromagnetic form factors. Importantly, they also enter into the two-body B
decay amplitudes described by QCD factorisation. They cannot be calculated from
first principles and are described by models based on a fixed-order conformal
expansion, which is not always sufficient in phenomenological applications. We
derive new models that are valid to all orders in the conformal expansion and
characterised by a small number of parameters related to experimental
observables.Motivated by the marginal agreement between the QCD factorisation
results with the experimental data, in particular for $B\to\pi\pi$, we
scrutinise the incalculable non-factorisable corrections to charmless
non-leptonic decays. We use the available results on $B\to\pi\pi$ to extract
information about the size and nature of the required non-factorisable
corrections that are needed to reconcile the predictions and data. We find that
the best-fit scenarios do not give reasonable agreement to $2\sigma$ until at
least a 40% non-factorisable contribution is added. Finally we consider the
exclusive $B\to V\gamma$ decays, where we analyse the recently updated
experimental data within QCD factorisation and present constraints on generic
supersymmetric models using the mass insertion approximation.
