Supernova remnants (SNRs) have great impact on the energy density and evolution of their galaxies. SNR shocks interact with the surrounding medium, compressing and heating it, as well as accelerating particles to cosmic ray (CR) energies. Most of the energy carried away by CRs is available to drive outflows in the interstellar medium (ISM), and thus they are a significant factor in galactic formation and evolution. That SNRs accelerate particles to CR energies is no longer in doubt, but there are many questions yet to be answered. We still lack detailed knowledge about the efficiency of the process of particle acceleration at SNR shocks, the effect of CR production on the evolution of SNRs, and the properties of magnetic fields in these systems and how these are amplified. Here I report on some recent work based on X-ray and gamma-ray observations of SNRs and how these shed light on the nature of the particle acceleration process in SNR shocks.