  In this short review we tried to give an outline of investigations of charged
pion condensation (PC) in dense baryonic (quark) matter in the framework of
effective Nambu--Jona-Lasinio (NJL) type models. The possibility of charged PC
phase in dense quark matter with isospin asymmetry is investigated. First, it
is demonstrated that this phase can be realized in the framework of massless
NJL model. But the existence of this phase is enormously fragile to the values
of current quark mass %.Then, and we show that charged PC phase is forbidden in
electrically neutral dense quark matter with $\beta$-equilibrium when current
quark masses are close to their physical value of 5.5 MeV. Nevertheless, then
it is shown that in real physical systems there could be conditions promoting
the appearance of charged PC phenomenon in dense quark matter, namely, it was
shown that if one includes into consideration the fact that system can have
finite size, then a dense charged PC phase can be realized there. It was also
demonstrated that the possibility of inhomogeneous pion condensate might allow
this phase to appear. And more recently it was revealed that there is another
interesting factor that can induce a charged PC phase in dense quark matter
even without isospin imbalance. It is a chiral imbalance of the system
(non-zero difference between densities of left- and right-handed quarks). This
results can be interesting in heavy ion collision experiments, where it is
expected to get high baryon densities. It is of interest also in the context of
the neutron stars, where quark matter might be realized in the core and very
high baryon and isospin densities are attained.
