  Galactic cosmic rays are widely believed to be accelerated in expanding shock
waves initiated by supernova explosions. The theory of diffusive shock
acceleration of cosmic rays is now well established, but two fundamental
questions remain partly unanswered: what is the acceleration efficiency, i.e.
the fraction of the total supernova energy converted to cosmic-ray energy, and
what is the maximum kinetic energy achieved by particles accelerated in
supernova explosions? Recent observations of supernova remnants, in X-rays with
the Chandra and XMM-Newton satellites and in very-high-energy gamma rays with
several ground-based atmospheric Cerenkov telescopes, have provided new pieces
of information concerning these two questions. After a review of these
observations and their current interpretations, I show that complementary
information on the diffusive shock acceleration process can be obtained by
studying the radio emission from extragalactic supernovae. As an illustration,
a nonlinear model of diffusive shock acceleration is applied to the radio light
curves of the supernova SN 1993J, which exploded in the nearby galaxy M81. The
results of the model suggest that most of the Galactic cosmic rays may be
accelerated during the early phase of interaction between the supernova ejecta
and the wind lost from the progenitor star.
