Radiative decays with light scalar mesons in initial or final state, phi(1020) -> gamma a_0(980), phi(1020) -> gamma f_0(980), a_0(980) -> gamma gamma, f_0(980) -> gamma gamma, f_0(980) (or a_0(980)) -> gamma rho(770) and f_0(980) (or a_0(980)) -> gamma omega(782) are studied in a unified approach. Amplitudes are calculated in one-loop approximation in framework of Resonance Chiral Theory. Contributions of pion and kaon loops are compared in various decays. Predictions of the model are compared with available data on scalar meson decays into two photons and radiative phi(1020)-meson decays. Calculated widths of decays f_0(980)/a_0(980) -> gamma rho(770)/omega(782) are not studied experimentally yet. Results for decay widths in q\bar{q} and qq \bar{q}\bar{q} models for the scalar meson structure are reviewed as well. The considered processes are of interest for current experimental programs in Frascati, Juelich and Novosibirsk.