Most of galactic cosmic rays are thought to be accelerated in supernova remnants by the diffusive shock acceleration mechanism. The data on cosmic rays at the Earth and the observation of non-thermal radiation from supernova remnants testify that the particles are accelerated with high efficiency and in a wide range of energies. We discuss the acceleration of ions and electrons by supernova shocks in a general context of the problem of cosmic ray origin. The emphasis is on the determination of the maximum energy limits for galactic sources and the transition from galactic to extragalactic cosmic rays.