  Recently it has been found that quantum chromodynamics (QCD) phase diagram
possesses a duality between chiral symmetry breaking and pion condensation. For
the first time this was revealed in the QCD motivated toy model. Then it was
demonstrated in effective models as well and new additional dualities being
found. We briefly recap the main features of this story and then discuss its
applications as a tool to explore the QCD phase structure. The most appealing
application is the possibility of getting the results on the QCD phase diagram
at large baryon density. Taking the idea from large $1/N_{c}$ universalities it
was argued that the scenario of circumventing the sign problem with the help of
dualities seems plausible. It is also discussed that there is a persistent
problem about whether there should be catalysis or anti-catalysis of chiral
symmetry breaking by chiral imbalance. One can probably say that the issue is
settled after lattice results (first principle approach), where the catalysis
was observed. But they used an unphysically large pion mass so it is still
interesting to get additional indications that this is the case. It is shown
just by the duality property that there exists catalysis of chiral symmetry
breaking. So, having in mind our results and the earlier lattice simulations,
one can probably claim that this issue is settled. It is demonstrated that the
duality can be used to obtain new results. As an example, it is showcased how
the phase structure of dense quark matter with chiral imbalance (with
possibility of inhomogeneous phases) can be obtained from the knowledge of a
QCD phase diagram with isopin asymmetry.
