In this talk, we will introduce an axial chemical potential $\mu_5$ as a trigger for parity breaking in a finite volume where the quark axial charge is approximately conserved. The Nambu--Jona-Lasinio model may be a sort of playground where parity-breaking effects (driven by a non-trivial $\mu_5$) can be investigated. A new phase with spontaneous breaking of parity is found and discussed together with analogies and differences with QCD. Next, we will study the lightest vector mesons via the VMD mechanism in the context of a parity-odd medium. We describe the new dispersion relation and introduce some experimental effects that could be observed in heavy ion experiments from vector meson decays into leptons. In particular, a very specific angular analysis of such decays may provide a significant signal that would unambiguously reveal the existence of parity-breaking.