  We discuss production of charm quarks, mesons as well as nonphotonic
electrons in $pp$ scattering at RHIC. The distributions in rapidity and
transverse momentum of charm and bottom quarks/antiquarks are calculated in the
$k_t$-factorization approach. The hadronization of heavy quarks is done by
means of fenomenological fragmentation functions and semileptonic decay
functions are found by fitting semileptonic decay data. Good description of the
inclusive data at large transverse momenta of electrons is obtained and a
missing strength at small transverse momenta of electrons is found.
  In addition we discuss kinematical correlations between charged leptons from
different mechanisms. Reactions initiated by purely QED
$\gamma^*\gamma^*$-fusion in elastic and inelastic $pp$ collisions as well as
diffractive mechanism of exclusive $c \bar c$ production are included. A good
description of the dilepton invariant mass spectrum of the PHENIX collaboration
is achieved. Distributions in the dilepton pair transverse momentum and in
azimuthal angle between electron and positron are presented.
  A new mechanism of exclusive production of $c \bar c$ is discussed.
Corresponding results are shown and the possibility of its identification is
discussed.
  We discuss also production of two pairs of $c \bar c$ within a simple
formalism of double-parton scattering (DPS). Very large cross sections,
comparable to single-$c \bar c$ production, are predicted for LHC energies.
Both total inclusive cross section as a function of energy and differential
distributions are shown. We discuss a perspective how to identify the double
scattering contribution.
