  We present results on rapidity and transverse momentum distributions of
inclusive charm quark production in hadronic and heavy-ion collisions at RHIC
and LHC energies, including the next-to-leading order, $O(\alpha_s^3)$,
radiative corrections and the nuclear shadowing effect. We determine hadronic
and nuclear K-factor for the differential and total inclusive cross sections
for the charm production. We discuss theoretical uncertainties inherent in our
calculation. In particular, we find that different extrapolations of gluon
density to low-$x$ region introduce large theoretical uncertainty in the
calculation of charm production at LHC energies. Finally, we comment on the
possibility of detecting the quark-gluon plasma signal as an enhanced charm
production in heavy-ion collisions at RHIC.
