  A brief overview on the theory and observations of relativistic particle
populations in clusters of galaxies is given. The following topics are
addressed: (i) the diffuse relativistic electron population within the
intra-cluster medium (ICM) as seen in the cluster wide radio halos and possibly
also seen in the high energy X-ray and extreme ultraviolet excess emissions of
some clusters, (ii) the observed confined relativistic electrons within fresh
and old radio plasma and their connection to cluster radio relics at cluster
merger shock waves, (iii) the relativistic proton population within the ICM,
and its observable consequences (if it exists), and (iv) the confined
relativistic proton population (if it exists) within radio plasma. The
importance of upcoming, sensitive gamma-ray telescopes for this research area
is highlighted.
