Under extreme conditions of high temperature and/or large quark (baryon) density, the vacuum of QCD changes its properties, and deconfinement, chiral symmetry restoration as well as chiral symmetry breaking take place. These transitions (phases) are accompanied by the rapid change in the rate and nature of topological transitions connecting different topological sectors. The heavy ion collisions (HIC) program opens a possibility to study these phenomena in so-called non-Abelian Quark-gluon plasma (QGP). In these phases the currents of light quarks (vector and axial-vector) can be independently examined for right-handed (RH) and left-handed (LH) quarks. To describe such a quark matter chiral chemical potential can be introduced to quantify the presence of chirality imbalance (ChI) i.e. the difference between the average numbers of RH and LH quarks in the fireball after HIC. In this review talk we will focus our attention on the discussion of the ChI related developments in heavy ion physics at central collisions and the plans for the future experiments aimed at establishing (or falsifying) the presence of Local spacial Parity Breaking (LPB) in heavy ion data. We describe some of experimental observables in detecting the signal of LPB. A number of measurements is proposed that allow to reach a definite conclusion on the occurrence of LPB effects in non-Abelian QGP produced in central heavy ion collisions and its simulation within a number of QCD-inspired models is outlined. Based on the effective meson theory in the presence of Chern-Simons interaction it is found that the spectrum of massive vector mesons splits into three polarization components with different effective masses. Moreover a resonance broadening occurs that leads to an increase of spectral contribution to the dilepton production as compared to the vacuum state. The asymmetry in production of longitudinally and transversely polarized states of ρ and ω mesons for various values of the dilepton invariant mass can serve as a characteristic indication of the LPB in CERES, HADES, PHENIX, STAR, NA60 and ALICE experiments.