  We investigate the physics of particle acceleration at non-relativistic
shocks exploiting two different and complementary approaches, namely a
semi-analytic modeling of cosmic-ray modified shocks and large hybrid (kinetic
protons/fluid electrons) simulations. The former technique allows us to extract
some information from the multi-wavelength observations of supernova remnants,
especially in the gamma-ray band, while the latter returns fundamental insights
into the details of particle injection and magnetic field amplification via
plasma instabilities. In particular, we present the results of large hybrid
simulations of non-relativistic shocks, discussing the properties of the
transition from the thermal to the non-thermal component, the spectrum of which
turns out to be the power-law predicted by first-order Fermi acceleration.
Along with a rather effective magnetic field amplification, we find that more
than 20% of the bulk energy is converted in non-thermal particles, altering
significantly the dynamics of the shock and leading to the formation of a
precursor.
