This paper reviews what physicists mean by chiral symmetry in quantum chromodynamics (QCD), why that symmetry is hidden in normal matter, and how it might be restored in hot or dense environments. The author starts by explaining chirality — a handedness property of quarks — and shows that a quark mass mixes right- and left-handed states. In the limit where the light quark masses vanish, chirality becomes a good quantum number. In the real world the up, down, and strange quarks are light but not massless: mu = 2.16 ± 0.07 MeV, md = 4.70 ± 0.07 MeV, and ms = 93.5 ± 0.8 MeV. Those small masses make chiral symmetry only approximate for the three lightest quarks.

To make these ideas concrete, the paper revisits the Dirac equation in a form that highlights chirality. It then covers spontaneous symmetry breaking — the idea that the QCD vacuum does not share the symmetry of the underlying equations — and the two ways a symmetry can be realized, called the Wigner and Nambu–Goldstone modes. Important formal points are included, such as the Nambu–Goldstone theorem and a remark on the U(1)A anomaly, which affects some expected symmetry relations. The author surveys several effective models used to study chiral symmetry: Nambu–Jona-Lasinio–type quark models with vector and axial-vector interactions, instanton-induced four- or six-quark interactions, a three-flavor linear sigma model with a determinant term (used to discuss the eta-prime mass), and a linear sigma model that includes parity-doublet nucleons.

At a conceptual level the review explains how mass and symmetry interact. For massless quarks chirality lines up with helicity (the direction of spin relative to motion). A nonzero mass mixes right- and left-handed components. The paper draws an analogy with superconductivity: the quark mass plays a role similar to the superconducting gap, but with an important difference. In superconductors the gap is generated dynamically. In QCD the notion of spontaneous breaking of chiral symmetry provides a mechanism for the quark mass to arise dynamically from the vacuum. A clear experimental signature of restored chiral symmetry would be spectral degeneracies between certain particle channels. In particular, the paper stresses that in the symmetric (Wigner) phase the sigma and pion channels should become degenerate, and the rho and a1 channels should also match.