Radio astronomy has changed. For years it studied relatively rare sources, which emit mostly non-thermal radiation across the entire electromagnetic spectrum, i.e. radio quasars and radio galaxies. Now it is reaching such faint flux densities that it detects mainly star-forming galaxies and the more common radio-quiet active galactic nuclei. These sources make up the bulk of the extragalactic sky, which has been studied for decades in the infrared, optical, and X-ray bands. I follow the transformation of radio astronomy by reviewing the main components of the radio sky at the bright and faint ends, the issue of their proper classification, their number counts, luminosity functions, and evolution. The overall big picture astrophysical implications of these results, and their relevance for a number of hot topics in extragalactic astronomy, are also discussed. The future prospects of the faint radio sky are very bright, as we will soon be flooded with survey data. This review should be useful to all extragalactic astronomers, irrespective of their favourite electromagnetic band(s), and even stellar astronomers might find it somewhat gratifying.
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