  We aim to test the plausibility of a theoretical framework in which the
$\gamma-$ray emission detected from supernova remnants is of hadronic origin,
i.e., due to the decay of neutral pions produced in nuclear collisions
involving relativistic nuclei. In particular, we investigate how the nature of
the circumstellar medium affects the evolution of a remnant and of its
$\gamma-$ray emission, stressing the role of magnetic field amplification in
the prediction of expected particle spectra. A phenomenological scenario
consistent with both the underlying Physics and the larger and larger amount of
observational data provided by the present generation of $\gamma-$ray
experiments is finally outlined and critically discussed.
