Symmetries and their dynamical and anomalous breakings play fundamental roles in physics. In particular, the symmetries of QCD at low energy are manifested in their most unambiguous form in the sector of light pseudoscalar mesons π0, η and η' While　π0 and  η are Goldstone bosons due to spontaneous chiral symmetry breaking, the η' is not due to the U(1)A anomaly. There is a second type of chiral anomaly driving the two-photon decays of these mesons. This system harbors information about the effects of SU(3) symmetry breaking and the mixing phenomena of the mesons due to isospin symmetry breaking. It provides a unique approach model independently to determine the light quark-mass ratio and the η-η' mixing angle, and represents a rich laboratory to study the origin and the dynamics of chiral symmetry breaking at low energy. In addition, the measurements of branching ratio or upper limits for various rare and forbidden decays of  η and η' will provide sensitive probes to test P, PC and C symmetries, and search for new physics beyond the Standard Model. A comprehensive experimental program has been developed at Jefferson Laboratory to perform high precision measurements of the two-photon decay widths and transition form factors at low Q2 on π0, η and η'  via the Primakoff effect. A new experimental proposal to study η and η'  rare decays is currently under development. An overview of these projects will be presented.