In this paper the current status of γ-ray observations of starburst galaxies from hundreds of MeV up to TeV energies with space-based instruments and ground-based Imaging Atmospheric Cherenkov Telescopes (IACTs) is summarised. The properties of the high-energy (HE; 100MeV ≤ E ≤ 100GeV) and very-high-energy (VHE; E ≥ 100GeV) emission of the archetypical starburst galaxies M82 and NGC253 are discussed and put into context with the HE γ-ray emission detected from other galaxies that show enhanced star-formation activity such as NGC4945 and NGC1068. Finally, prospects to study the star-formation – γ-ray emission connection from Galactic systems to entire galaxies with the forthcoming Cherenkov Telescope Array (CTA) are outlined.

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