  Cosmic-rays are ubiquitous, but their origins are surprisingly difficult to
understand. A review is presented of some of the basic issues common to cosmic
particle accelerators and arguments leading to the likely importance of
diffusive shock acceleration as a general explanation. The basic theory of
diffusive shock acceleration is outlined, followed by a discussion of some of
the key issues that still prevent us from a full understanding of its outcomes.
Some recent insights are mentioned at the end that may help direct ultimate
resolution of our uncertainties.
