The origin of cosmic rays (CRs) has puzzled scientists since the pioneering discovery by Victor Hess in 1912. In the last decade, however, modern supercomputers have opened a new window on the processes regulating astrophysical collisionless plasmas, allowing the study of CR acceleration via first-principles kinetic simulations; at the same time, new generations of X-ray and gamma-ray telescopes have been collecting evidence that Galactic CRs are accelerated in the blast waves of supernova remnants (SNRs).

I present state-of-the-art particle-in-cells simulations of non-relativistic shocks, in which ion and electron acceleration efficiency, and magnetic field amplification, are studied in detail as a function of the shock parameters. I then discuss the theoretical and observational counterparts of these findings, comparing them with predictions of diffusive shock acceleration theory, and with multi-wavelength observations of young SNRs.