The theoretical structure of the pion-photon interaction amplitudes at low energies and the possibility of studying them experimentally are reviewed. It is pointed out that it is possible to measure the $\pi\pi$ scattering lengths in photon-pion transitions. For processes involving an odd number of pions, a discussion is given of the fundamental role of the $\pi^0\to2\gamma$ decay amplitude, which determines the form of all more complex amplitudes. This fact is connected with the anomalies in the axial-vector current that appears in the weak interaction. In processes involving an even number of pions, the radius and polarizability of the $\pi^-$ meson appear as basic parameters. The polarizability is related to the weak decay amplitude.