  Motivated by recent unsuccessful efforts to detect the predicted flux of TeV
gamma-rays from supernova remnants, we present a critical examination of the
theory on which these predictions are based. Three crucial problems are
identified: injection, maximum achievable particle energy and spectral index.
In each case significant new advances in understanding have been achieved,
which cast doubt on prevailing paradigms such as Bohm diffusion and
single-fluid MHD. This indicates that more realistic analytical models, backed
by more sophisticated numerical techniques should be employed to obtain
reliable predictions. Preliminary work on incorporating the effects of
anomalous transport suggest that the resulting spectrum should be significantly
softer than that predicted by conventional theory.
