  Starburst galaxies have a highly increased star-formation rate compared to
regular galaxies and inject huge amounts of kinetic power into the interstellar
medium via supersonic stellar winds, and supernova explosions. Supernova
remnants, which are considered to be the main source of cosmic rays (CRs), form
an additional, significant energy and pressure component and might influence
the star-formation process in a major way. Observations of starburst galaxies
at \gamma-ray energies gives us the unique opportunity to study non-thermal
phenomena associated with hadronic CRs and their relation to the star-formation
process. In this work, recent observations of starburst galaxies with space and
ground-based \gamma-ray telescopes are being reviewed and the current state of
theoretical work on the \gamma-ray emission is discussed. A special emphasis is
put on the prospects of the next-generation Cherenkov Telescope Array for the
study of starburst galaxies in particular and star-forming galaxies in general.
