  Diffusive shock acceleration (DSA) is now widely accepted as the model to
explain the production of cosmic rays (CRs) in a wide range of astrophysical
environments. Despite initial successes of the theory in explaining the
energetics and the spectrum of CRs accelerated by supernova remnants, there
still remain some unresolved issues such as particle injection out of the
thermal plasma at shocks, CR diffusion due to the self-generated MHD waves and
yet-to-be-detected gamma-ray emission due to the ionic CRs. Recent technical
advancements to resolve these issues are reviewed.
