The main challenge in computing inclusive cross sections and decay spectra in QCD is posed by kinematic thresholds.
The threshold region is characterized by stringent phase–space constraints that are reflected in large perturbative
corrections due to soft and collinear radiation as well as large non-perturbative effects. Major progress in addressing
this problem was made in recent years by Dressed Gluon Exponentiation (DGE), a formalism that combines Sudakov
and renormalon resummation in moment space. DGE has proven effective in extending the range of applicability
of perturbation theory well into the threshold region and in identifying the relevant non-perturbative corrections.
Here we review the method from a general perspective using examples from deep inelastic structure functions, event–
shape distributions, heavy–quark fragmentation and inclusive decay spectra. A special discussion is devoted to the
applications of DGE to radiative and semileptonic B decays that have proven valuable for the interpretation of data
from the B factories
