We present an investigation of radio luminosity functions (LFs) and number counts based on the Karl G. Jansky Very Large Array- COSMOS 3 GHz Large Project. The radio-selected sample of 7826 galaxies with robust optical/near-infrared counterparts with excellent photometric coverage allows us to construct the total radio LF since z _ 5:7. Using the Markov chain Monte Carlo algorithm, we fit the redshift dependent pure luminosity evolution model to the data and compare it with previously published VLA-COSMOS LFs obtained on individual populations of radio-selected star-forming galaxies and galaxies hosting active galactic nuclei classified on the basis of presence or absence of a radio excess with respect to the star- formation rates derived from the infrared emission. We find they are in excellent agreement, thus showing the reliability of the radio excess method in selecting these two galaxy populations at radio wavelengths. We study radio number counts down to submicrojansky levels drawn from different models of evolving LFs. We show that our evolving LFs are able to reproduce the observed radio sky brightness, even though we rely on extrapolations toward the faint end. Our results also imply that no new radio-emitting galaxy population is present below 1 _Jy. Our work suggests that selecting galaxies with radio flux densities between 0.1 and 10 _Jy will yield a star-forming galaxy in 90–95% of the cases with a high percentage of these galaxies existing around a redshift of z _ 2, thus providing useful constraints for planned surveys with the Square Kilometer Array and its precursors.