  Gaia Data Release 3 (Gaia DR3) contains the second release of the combined
radial velocities. It is based on the spectra collected during the first 34
months of the nominal mission. The longer time baseline and the improvements of
the pipeline made it possible to push the processing limit, from Grvs = 12 in
Gaia DR2, to Grvs = 14 mag. In this article, we describe the new
functionalities implemented for Gaia DR3, the quality filters applied during
processing and post-processing and the properties and performance of the
published velocities. For Gaia DR3, several functionalities were upgraded or
added. (Abridged) Gaia DR3 contains the combined radial velocities of 33 812
183 stars. With respect to Gaia DR2, the interval of temperature has been
expanded from Teff \in [3600, 6750] K to Teff \in [3100, 14500] K for the
bright stars ( Grvs \leq 12 mag) and [3100, 6750] K for the fainter stars. The
radial velocities sample a significant part of the Milky Way: they reach a few
kilo-parsecs beyond the Galactic centre in the disc and up to about 10-15 kpc
vertically into the inner halo. The median formal precision of the velocities
is of 1.3 km/s at Grvs = 12 and 6.4 km/s at Grvs = 14 mag. The velocity zero
point exhibits a small systematic trend with magnitude starting around Grvs =
11 mag and reaching about 400 m/s at Grvs = 14 mag. A correction formula is
provided, which can be applied to the published data. The Gaia DR3 velocity
scale is in satisfactory agreement with APOGEE, GALAH, GES and RAVE, with
systematic differences that mostly do not exceed a few hundreds m/s. The
properties of the radial velocities are also illustrated with specific objects:
open clusters, globular clusters as well as the Large Magellanic Cloud (LMC).
For example, the precision of the data allows to map the line-of-sight
rotational velocities of the globular cluster 47 Tuc and of the LMC.
