Starburst galaxies are thought to form when two galaxies interact and sometimes merge. These unique objects have high star-formation rates and hence high supernova rates, as well as large reservoirs of very dense gas. Assuming galactic cosmic rays originate in supernovae, starburst galaxies should contain copious quantities of cosmic rays that produce diffuse very-high-energy (VHE; E>100 GeV) gamma-ray emission via their interaction with the gaseous material. VERITAS, an array of 12-m atmospheric-Cherenkov telescopes in Arizona, USA, was used to detect VHE emission from the starburst galaxy M 82 during deep observations in 2008-09. However, the initial VERITAS detection was weak and much deeper observations were needed to draw strong conclusions regarding the underlying emission and transport processes. Accordingly, VERITAS was used to perform an extensive observation campaign on M 82 and approximately 335 hours of data were taken. Several other starburst galaxies were also observed in the past few years. A brief summary of the results from these starburst-galaxy observations is presented here.