Modelling Hard $\gamma$-Ray Emission From Supernova Remnants

The observation by the CANGAROO experiment of TeV emission from SN 1006, in conjunction with several instances of non-thermal X-ray emission from supernova remnants, has led to inferences of super-TeV electrons in these extended sources. While this is sufficient to propel the theoretical community in their modelling of particle acceleration and associated radiation, the anticipated emergence in the next decade of a number of new experiments probing the TeV and sub-TeV bands provides further substantial motivation for modellers. In particular, the quest for obtaining unambiguous gamma-ray signatures of cosmic ray ion acceleration defines a ``Holy Grail'' for observers and theorists alike. This review summarizes theoretical developments in the prediction of MeV-TeV gamma-rays from supernova remnants over the last five years, focusing on how global properties of models can impact, and be impacted by, hard gamma-ray observational programs, thereby probing the supernova remnant environment. Properties of central consideration include the maximum energy of accelerated particles, the density of the unshocked interstellar medium, the ambient magnetic field, and the relativistic electron-to-proton ratio. Criteria for determining good candidate remnants for observability in the TeV band are identified