Galactic cosmic rays are widely believed to be accelerated at the expanding shock waves
of supernova remnants (SNRs). Diffusive shock acceleration, a well-developed theory of
the acceleration process at work in SNRs, lays the foundation for the SNR paradigm of
the cosmic-ray origin,  though key problems are yet to be solved. After reviewing the
current status of this field, I will present our work on X-ray and GeV gamma-ray
observations of SNRs, and discuss prospect for ASTRO-H.