  Due to observations made by the Compton Gamma-Ray Observatory over the last
six years, it appears that a number of galactic supernova remnants may be
candidates for sources of cosmic gamma-rays. These include shell-type remnants
such as IC443 and $\gamma$ Cygni, which have no known parent pulsars, but have
significant associations with unidentified EGRET sources, and others that
appear to be composite, where a pulsar is embedded in a shell (e.g. W44 and
Vela), or are purely pulsar-driven, such as the Crab Nebula. This review
discusses our present understanding of gamma-ray production in plerionic and
non-plerionic supernova remnants, and explores the relationship between such
emission and that in other wavebands. Focuses include models of the Crab and
Vela nebulae, the composite nature of W44, the relationship of shell-type
remnants to cosmic ray production, the relative importance of shock-accelerated
protons and electrons, constraints on models placed by TeV, X-ray and radio
observations, and the role of electrons injected directly into the remnants by
parent pulsars.
