Star-formation and the Starburst phenomenon are presented with respect to a number of nearby star-forming galaxies where our understanding of the process can be calibrated. Methods of estimating star-formation rates are discussed together with the role played in the investigation of the process by multi-wavelength studies of a few selected starburst galaxies (especially the well studied galaxy M82). Our understanding of nearby systems allows us to study the star-formation history of the Universe by observing high-redshift starburst galaxies. These begin to dominate the radio source populations at centimetric wavelengths at flux densities below a few 10s of Jy. New very sensitive, high resolution telescopes in the sub-mm and radio will revolutionize our understanding of these distant star-forming systems, some of which may contain embedded AGN.

15 pages, 19 figures, To appear in the proceedings of `The 8th European VLBI Network Symposium on New Developments in VLBI Science and Technology', ed. A. Marecki et al., held in Torun, Poland, on September 26-29, 2006 (Invited Review)