There is now good agreement between the various methods of estimating the space density of the star-formation rate (SFRD) at low redshifts (z < 1), with uncertainties around 30–50%. However, the situation at higher redshifts remains much less clear, with uncertainties in the SFRD, due to e.g. poorly known dust absorption corrections, of as much as 300–500%. Radio emission from star-forming galaxies is unaffected by absorption and scales linearly with star-formation rate, thus the radio luminosity of star-forming galaxies provides an excellent independent, unbiased measure of their star-formation rate. The current deepest ‘blank field’ radio surveys (reaching <10 μJy rms at 1.4 GHz) are sensitive enough to detect starburst galaxies out to z ~ 3, and so potentially offer an excellent way to measure the SFRD. Indeed, modelling of the sub-mJy source counts requires an additional population of faint steep spectrum objects, that are very likely to be starburst galaxies.