  We discuss production of charmed mesons as well as electrons/muons from
semileptonic decays of charm and bottom mesons in proton-proton collisions at
the LHC. The cross section for inclusive production of $c \bar c$ and $b \bar
b$ pairs is calculated in the framework of the $k_{\perp}$-factorization
approach. Here, the KMR and Jung CCFM unintegrated gluon distribution functions
are used. Theoretical uncertainties of the model related to the choice of
renormalization and factorization scales as well as due to the quark mass are
also discussed. The hadronization of charm and bottom quarks is included within
the fragmentation functions technique. Inclusive differential distributions in
transverse momentum of charmed mesons are presented and compared to recent
results of the ALICE collaboration. Furthermore, we also consider production of
different $D \bar D$ pairs in unique kinematics of forward rapidities of the
LHCb experiment. Kinematical correlations in azimuthal angle $\varphi_{D\bar
D}$ and invariant mass $M_{D \bar D}$ distributions are presented and compared
to LHCb data. Furthermore, the semileptonic decays of charm and bottom mesons
are done with the help of decay functions found by fitting recent semileptonic
data obtained by the CLEO and BABAR collaborations. Inclusive differential
distributions in transverse momentum of leptons for several kinematical regions
are presented and compared to recent results of the ALICE and CMS
collaborations.
