  We report on recent theoretical progress in radiative B decays. We focus on a
calculation of logarithmically enhanced QED corrections to the branching ratio
and forward-backward asymmetry in the inclusive rare decay anti-B --> X(s) l+
l-, and present the results of a detailed phenomenological analysis. We also
report on the calculation of NNLO QCD corrections to the inclusive decay anti-B
--> X(s) gamma. As far as exclusive modes are concerned we consider
transversity amplitudes and the impact of right-handed currents in the
exclusive anti-B --> K^* l+ l- decay. Finally, we state results for exclusive B
--> V gamma decays, notably the time-dependent CP-asymmetry in the exclusive B
--> K^* gamma decay and its potential to serve as a so-called ``null test'' of
the Standard Model, and the extraction of CKM and unitarity triangle parameters
from B --> (rho,omega) gamma and B --> K^* gamma decays.
