Production of $c \bar c$ pairs at LHC: $k_t$-factorization and double-parton scattering

We discuss charm production at LHC. The production of single $c \bar c$ pairs is calculated in the $k_t$-factorization approach. We use several unintegrated gluon distributions from the literature. Differential distributions for several charmed mesons are presented and compared to recent results of the ALICE and LHCb collaborations. Some missing strength can be observed. Furthermore we discuss production of two $c \bar c$ pairs within a simple formalism of double-parton scattering (DPS). Surprisingly large cross sections, comparable to single-parton scattering (SPS) contribution to $c \bar c$ production, are predicted for LHC energies