  Galactic cosmic rays are commonly believed to be accelerated at supernova
remnants via diffusive shock acceleration. Despite the popularity of this idea,
a conclusive proof for its validity is still missing. Gamma-ray astronomy
provides us with a powerful tool to tackle this problem, because gamma rays are
produced during cosmic ray interactions with the ambient gas. The detection of
gamma rays from several supernova remnants is encouraging, but still does not
constitute a proof of the scenario, the main problem being the difficulty in
disentangling the hadronic and leptonic contributions to the emission. Once
released by their sources, cosmic rays diffuse in the interstellar medium, and
finally escape from the Galaxy. The diffuse gamma-ray emission from the
Galactic disk, as well as the gamma-ray emission detected from a few galaxies
is largely due to the interactions of cosmic rays in the interstellar medium.
On much larger scales, cosmic rays are also expected to permeate the
intracluster medium, since they can be confined and accumulated within clusters
of galaxies for cosmological times. Thus, the detection of gamma rays from
clusters of galaxies, or even upper limits on their emission, will allow us to
constrain the cosmic ray output of the sources they contain, such as normal
galaxies, AGNs, and cosmological shocks. In this paper, we describe the impact
that the Cherenkov Telescope Array, a future ground-based facility for
very-high energy gamma-ray astronomy, is expected to have in this field of
research.
