Cosmic rays interacting with the interstellar medium (ISM) give rise
to the emission of gamma-rays over a wide range of energies. The
main processes are bremsstrahlung and inverse Compton scattering of
electrons, and
decay subsequent to hadronic interactions of
protons and nuclei. Thus, observations of the diffuse galactic
gamma-ray emission, together with measurements of the arriving
cosmic-ray flux, provide a unique probe of the distribution of both
the ISM and the cosmic rays within the Galaxy. Observations with
EGRET below 1GeV agree well with models of the distribution of
interstellar matter ([Hunter et al. 1997]). At higher energies, the
observed gamma-ray intensity exceeds the model predictions by
50%. This excess could be due to unresolved point sources
below the EGRET detection threshold, or it may reflect limitations in
our understanding of cosmic rays, such as a local cosmic-ray spectrum
which is not representative of the galactic average. VERITAS will
measure the differences in the diffuse emission spectrum from
different regions of the galaxy with excellent accuracy up to the TeV
range, providing the first measurement of the cosmic-ray distribution
in our galaxy at such high energies. Together with results from
GLAST, a comprehensive and consistent picture of particle interactions
with the ISM should evolve.