  The nature of the light scalar mesons is one of the most intriguing open
challenges in hadronic spectroscopy. It is argued that radiative decays
involving these scalars can serve as an important decisive tool in establishing
their nature. In particular, special emphasis is made on the radiative decays
of the scalars themselves (in addition to the radiative decays of the phi-meson
with the scalars appearing in the final state), including their two-photon
decays. All the above mentioned processes are considered in detail in the
(point-like) kaon molecule model of the scalars and explicit predictions for
the decay widths are made. In addition, finite-range corrections to the
point-like results are investigated, with a special attention payed to gauge
invariance of the decay amplitude. Finally, the conclusion is made that
experimental data on the radiative decays with the light scalar mesons involved
strongly support the molecule assignment for the latter.
