We have made the first detailed study of the high-frequency radio-source population in the local universe, using a sample of 202 radio sources from the Australia Telescope 20 GHz (AT20G) survey identified with galaxies from the 6dF Galaxy Survey (6dFGS). The AT20G-6dFGS galaxies have a median redshift of z=0.058 and span a wide range in radio luminosity, allowing us to make the first measurement of the local radio luminosity function at 20 GHz. Our sample includes some classical FR-1 and FR-2 radio galaxies, but most of the AT20G-6dFGS galaxies host compact (FR-0) radio AGN which appear lack extended radio emission even at lower frequencies. Most of these FR-0 sources show no evidence for relativistic beaming, and the FR-0 class appears to be a mixed population which includes young Compact Steep-Spectrum (CSS) and Gigahertz-Peaked Spectrum (GPS) radio galaxies. We see a strong dichotomy in the Wide-field Infrared Survey Explorer (WISE) mid-infrared colours of the host galaxies of FR-1 and FR-2 radio sources, with the FR-1 systems found almost exclusively in WISE `early-type galaxies and the FR-2 radio sources in WISE `late-type galaxies. The host galaxies of the flat- and steep-spectrum radio sources have a similar distribution in both K--band luminosity and WISE colours, though galaxies with flat-spectrum sources are more likely to show weak emission lines in their optical spectra. We conclude that these flat-spectrum and steep-spectrum radio sources mainly represent different stages in radio-galaxy evolution, rather than beamed and unbeamed radio-source populations.
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