The major advantage of using radio observations for determining the star formation history of the universe is no need for uncertain dust-extinction corrections. Radio emission at 1.4 GHz (20cm) is dominated by the emission from active-galactic nuclei (AGN) and star-forming (SF) galaxies, hence a reliable SF/AGN separation is one of the main pre-requisites for a robust determination of star-formation rates using radio-data. The VLA-COSMOS survey with ~3,600 detected radio sources at 1.4GHz, with 1.5" resolution and high sensitivity (rms = 10 uJy/beam), provides enough targets to allow for the first time for a robust systematic characterization of the 'cosmological mix' of faint radio sources. Utilizing the entire COSMOS multi-wavelength (X-ray to radio) data set I will present our method which separates the radio population into SF and AGN galaxies. Our first results indicate that SF galaxies are not the dominant radio population at faint flux densities (<1 mJy) as previously suspected, but rather have a fairly constant contribution with decreasing fluxes. Selecting the SF galaxies within the VLA-COSMOS population, we derive their star formation rates and present the dust-unbiased cosmic star-formation history out to z=1, for the first time based on radio observations of a large, contiguous field with unprecedented sensitivity. I will also discuss the evolution of the 1.4 GHz luminosity function out to z=1, separately for SF and AGN dominated galaxies.