  We discuss the production of charmonium and open charm in nuclear collisions
at SPS/FAIR energies within the framework of the statistical hadronization
model. The increasing importance at lower energies of Lambda_c production is
discussed and provides a challenge for future experiments. We also show that
possible modifications of charmed hadrons in the hot hadronic medium do not
lead to measurable changes in the cross sections for D-meson production. A
possible influence of medium effects can be seen, however, in yields of
charmonium. These effects are visible at all energies and results will be
presented for the energy range between charm threshold and RHIC energy.
