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The GaLactic and Extragalactic All-sky Murchison Widefield Array (GLEAM) is a radio continuum survey at 76–227 MHz of the entire southern sky (Declination 
$<\!{+}30^{\circ}$
) with an angular resolution of 
${\approx}2$
arcmin. In this paper, we combine GLEAM data with optical spectroscopy from the 6dF Galaxy Survey to construct a sample of 1 590 local (median 
$z \approx 0.064$
) radio sources with 
$S_{200\,\mathrm{MHz}} > 55$
mJy across an area of 
${\approx}16\,700\,\mathrm{deg}^{2}$
. From the optical spectra, we identify the dominant physical process responsible for the radio emission from each galaxy: 73% are fuelled by an active galactic nucleus (AGN) and 27% by star formation. We present the local radio luminosity function for AGN and star-forming (SF) galaxies at 200 MHz and characterise the typical radio spectra of these two populations between 76 MHz and 
${\sim}1$
GHz. For the AGN, the median spectral index between 200 MHz and 
${\sim}1$
GHz, 
$\alpha_{\mathrm{high}}$
, is 
$-0.600 \pm 0.010$
(where 
$S \propto \nu^{\alpha}$
) and the median spectral index within the GLEAM band, 
$\alpha_{\mathrm{low}}$
, is 
$-0.704 \pm 0.011$
. For the SF galaxies, the median value of 
$\alpha_{\mathrm{high}}$
is 
$-0.650 \pm 0.010$
and the median value of 
$\alpha_{\mathrm{low}}$
is 
$-0.596 \pm 0.015$
. Among the AGN population, flat-spectrum sources are more common at lower radio luminosity, suggesting the existence of a significant population of weak radio AGN that remain core-dominated even at low frequencies. However, around 4% of local radio AGN have ultra-steep radio spectra at low frequencies (
$\alpha_{\mathrm{low}} < -1.2$
). These ultra-steep-spectrum sources span a wide range in radio luminosity, and further work is needed to clarify their nature.
In this paper, we describe the system design and capabilities of the Australian Square Kilometre Array Pathfinder (ASKAP) radio telescope at the conclusion of its construction project and commencement of science operations. ASKAP is one of the first radio telescopes to deploy phased array feed (PAF) technology on a large scale, giving it an instantaneous field of view that covers 
$31\,\textrm{deg}^{2}$ at 
$800\,\textrm{MHz}$. As a two-dimensional array of 36
$\times$12 m antennas, with baselines ranging from 22 m to 6 km, ASKAP also has excellent snapshot imaging capability and 10 arcsec resolution. This, combined with 288 MHz of instantaneous bandwidth and a unique third axis of rotation on each antenna, gives ASKAP the capability to create high dynamic range images of large sky areas very quickly. It is an excellent telescope for surveys between 700 and 
$1800\,\textrm{MHz}$ and is expected to facilitate great advances in our understanding of galaxy formation, cosmology, and radio transients while opening new parameter space for discovery of the unknown.
