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.