It has been known for nearly a century that the Earth is constantly being bombarded by, to quote from the 1912 discovery paper, 'an ionizing radiation of extreme penetrating power' and extraterrestrial origin. These cosmic ray particles are now known to extend in energy right up to at least 1020 eV. This is a macroscopic amount of energy, in fact some 16 J, but all the evidence points to this being carried by ordinary atomic nuclei including protons. Such extreme events are, however, very rare and the bulk of the cosmic rays have more moderate, but still very high, energies.The theory of diffusive shock acceleration, a variant of Fermi acceleration operating at strong collisionless plasma shocks, is currently the best bet for explaining the origin of the cosmic rays. This talk will describe our current understanding of this acceleration process and the observational situation. Some interesting plasma physics questions to do with the acceleration process will also be discussed. While great progress has been made it seems unlikely that the problem of the origin of cosmic rays will be regarded as completely solved by the centenary of their discovery in 2012.