We predict the evolution of the radio continuum sky at 1.4 GHz from the Horizon-AGN Adaptive Mesh Refinement (AMR) cosmological hydrodynamical simulation of a cubic volume of the Universe 100h−1 Mpc on a side. With empirically motivated models for the radio continuum emission due to both star formation and Active Galactic Nuclei (AGN), we estimate the contribution of each of these processes to the local radio continuum luminosity function (LF) and describe its evolution up to redshift 4. Despite the simplicity of these models, we find that our predictions for the local luminosity function are fairly consistent with Mauch & Sadler (2007) observations, with the faint end of the luminosity function dominated by star forming galaxies and the bright end by radio loud AGNs. At redshift one, a decent match to Smolcic et al. (2009) VLA data in the COSMOS field can only be achieved when we account for radio continuum emission from AGNs. We predict that the strongest evolution across the peak epoch of cosmic activity happens for low luminosity star forming galaxies L1.4GHz 1024 W Hz−1 show surprisingly little evolution from z = 0 to z = 4.