  We provide a model-independent framework for the analysis of the radiative
B-meson decays B -> K* gamma and B -> rho gamma. In particular, we give a
systematic discussion of the various contributions to these exclusive processes
based on the heavy-quark limit of QCD. We propose a novel factorization formula
for the consistent treatment of B -> V gamma matrix elements involving charm
(or up-quark) loops, which contribute at leading power in Lambda_QCD/m_B to the
decay amplitude. Annihilation topologies are shown to be power suppressed. In
some cases they are nevertheless calculable. The approach is similar to the
framework of QCD factorization that has recently been formulated for two-body
non-leptonic B decays. These results allow us, for the first time, to compute
exclusive b -> s(d) gamma decays systematically beyond the leading logarithmic
approximation. We present results for these decays complete to next-to-leading
order in QCD and to leading order in the heavy-quark limit. Phenomenological
implications for various observables of interest are discussed, including
direct CP violation, and isospin and U-spin breaking effects.
