  We review one-particle inclusive production of heavy-flavored hadrons in a
framework which resums the large collinear logarithms through the evolution of
the FFs and PDFs and, at the same time, retains the full dependence on the
heavy-quark mass without additional theoretical assumptions. The main focus is
on the production of D^* mesons in deep inelastic electron--proton scattering
at HERA. We show results, neglecting for the time being the heavy-quark mass
terms, for deep inelastic D^* meson production at finite transverse momenta.
Work to implement this process in the above mentioned massive QCD framework is
in progress.
