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.
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