  We discuss hadroproduction of open charmed mesons ($D^0$, $D^{\pm}$,
$D^{\pm}_{S}$) at the LHC energy $\sqrt{s} = 7$ TeV. The cross section for
inclusive production of $c \bar c$ pairs is calculated within the
$k_{\perp}$-factorization (or high-energy factorization) approach which
effectively includes higher-order corrections. Results of the
$k_{\perp}$-factorization approach are compared to NLO parton model
predictions. The hadronization of charm quarks is included with the help of the
Peterson fragmentation functions. Inclusive differential distributions in
(pseudo)rapidity and transverse momentum for several charmed mesons are
calculated and compared to recent results of the ALICE, ATLAS and LHCb
experiments. We also take into consideration a mechanism of double charm (two
pairs of $c \bar c$) production within a simple formalism of double-parton
scattering (DPS). Surprisingly for LHC energies the DPS cross sections are
found to be larger than those from the standard SPS mechanism. We compare our
predictions for $DD$ meson-meson pair production with recent measurements of
the LHCb collaboration, including correlation observables. Our calculations
clearly confirm the dominance of DPS in the production of double charm, however
some strength seems to be still lacking. Possible missing contribution from the
so-called single-ladder-splitting DPS mechanism is also discussed.
