From E. Fermi to Fermi-LAT: watching particle acceleration in supernova
  remnants
  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
