Supernova remnants (SNRs) have been regarded for many decades as the sources of Galactic cosmic rays (CRs) up to a few PeV. However, only with the advent of Fermi-LAT it has been possible to detect - at least in some SNRs - \gamma-rays whose origin is unequivocally hadronic, namely due to the decay of neutral pions produced by collisions between relativistic nuclei and the background plasma. When coupled with observations in other bands (from radio to TeV \gamma-rays), Fermi-LAT data present evidence for CR spectra significantly steeper than the standard prediction of diffusive shock acceleration, forcing us to rethink our theoretical understanding of efficient particle energization at strong shocks.

We outline how, by including the effects of CR-triggered magnetic field amplification, it is possible to reconcile non-linear models of diffusive shock acceleration with \gamma-ray observations, in particular providing a successful application of such a theory to Tycho's SNR. Finally, we show how kinetic simulations can investigate the microphysics of the non-linear coupling of accelerated particles and magnetic fields, probing from first principles the efficiency of the Fermi mechanism at strong shocks.