Résumé
Context. 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 G<SUB>RVS</SUB> = 12 in Gaia DR2 to G<SUB>RVS</SUB> = 14 mag. <BR /> Aims: 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. <BR /> Methods: For Gaia DR3, several functionalities were upgraded or added to the spectroscopic pipeline. The calibrations were improved in order to better model the temporal evolution of the straylight and of the instrumental point spread function (PSF). The overlapped spectra, which were mostly discarded in Gaia DR2, are now handled by a dedicated module. The hot star template mismatch, which prevented publication of hot stars in Gaia DR2, is largely mitigated now, down to G<SUB>RVS</SUB> = 12 mag. The combined radial velocity of stars brighter than or equal to G<SUB>RVS</SUB> = 12 mag is calculated in the same way as in Gaia DR2, that is, as the median of the epoch radial velocity time series. The combined radial velocity of the fainter stars is measured from the average of the cross-correlation functions. <BR /> Results: Gaia DR3 contains the combined radial velocities of 33 812 183 stars. With respect to Gaia DR2, the temperature interval has been expanded from T<SUB>eff</SUB> ∈ [3600, 6750] K to T<SUB>eff</SUB> ∈ [3100, 14 500] K for the bright stars (G<SUB>RVS</SUB> ≤ 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 kiloparsecs 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 1.3 km s<SUP>−1</SUP> at G<SUB>RVS</SUB> = 12 and 6.4 km s<SUP>−1</SUP> at G<SUB>RVS</SUB> = 14 mag. The velocity zeropoint exhibits a small systematic trend with magnitude that starts around G<SUB>RVS</SUB> = 11 mag and reaches about 400 m s<SUP>−1</SUP> at G<SUB>RVS</SUB> = 14 mag. A correction formula is provided that can be applied to the published data. The Gaia DR3 velocity scale agrees satisfactorily with APOGEE, GALAH, GES, and RAVE; the systematic differences mostly remain below a few hundred m s<SUP>−1</SUP>. The properties of the radial velocities are also illustrated with specific objects: open clusters, globular clusters, and the Large Magellanic Cloud. For example, the precision of the data allows mapping the line-of-sight rotational velocities of the globular cluster 47 Tuc and of the Large Magellanic Cloud.