Radio wavelengths offer the unique possibility of tracing the total star-formation rate in galaxies, both obscured and unobscured. As such, they may provide the most robust measurement of the star-formation history of the Universe. In this chapter we highlight the constraints that the SKA can place on the evolution of the star-formation history of the Universe, the survey area required to overcome sample variance, the spatial resolution requirements, along with the multi-wavelength ancillary data that will play a major role in maximising the scientific promise of the SKA. The required combination of depth and resolution means that a survey to trace the star formation in the Universe should be carried out with a facility that has a resolution of at least ~0.5arcsec, with high sensitivity at < 1 GHz. We also suggest a strategy that will enable new parameter space to be explored as the SKA expands over the coming decade.
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