Cosmic rays are relativistic charged particles (mainly protons and a small fraction of heavier nuclei) hitting Earth from outer space. According to the most popular model for their origin, galactic cosmic rays are accelerated at the outer front of expanding supernova remnants, via the so- called diffusive shock acceleration mechanism. Even though the predictions of this model seem to broadly fit the general picture emerging from observations, we are still waiting for the conclusive proof that supernovae are the sources of galactic cosmic rays.Such final proof might come from the recent detections of some supernova remnants in very high- energy gamma rays with the HESS telescope. The production of such energetic photons is expected, due to interactions between cosmic ray protons and the interstellar matter surrounding the supernova remnant. However, since other competing (e.g. leptonic) processes can also generate gamma rays, an accurate modelling of the acceleration of particles and of the accompanying radiation is needed in order to disentangle the different contributions and possibly solve the old standing problem of the origin of cosmic rays.