Cepheids are pulsating stars that play a crucial role in several astrophysical contexts. Among the different types, the Classical Cepheids are fundamental tools for the calibration of the extragalactic distance ladder. They are also powerful stellar population tracers in the context of Galactic studies. The Gaia Third Data Release (DR3) publishes improved data on Cepheids collected during the initial 34 months of operations. We present the Gaia DR3 catalogue of Cepheids of all types, obtained through the analysis carried out with the Specific Object Study (SOS) Cep&RRL pipeline. We discuss the procedures adopted to clean the Cepheid sample from spurious objects, to validate the results, and to re-classify sources with a wrong outcome from the SOS Cep&RRL pipeline. The Gaia DR3 includes multi-band time-series photometry and characterisation by the SOS Cep&RRL pipeline for a sample of 15006 Cepheids of all types. The sample includes 4663, 4616, 321 and 185 pulsators, distributed in the LMC, SMC, M31 and M33, respectively, as well as 5221 objects in the remaining All Sky sub-region which includes stars in the MW field/clusters and in a number of small satellites of our Galaxy. Among this sample, 327 objects were known as variable stars in the literature but with a different classification, while, to the best of our knowledge, 474 stars have not been reported before to be variable stars and therefore they likely are new Cepheids discovered by Gaia.

Cone search capability for table J/A+A/674/A17/table5 (Re-processing of the Gaia DR3 data for multi-mode Classical Cepheids not detected as such by the Specific Object Studies (SOS) Cep&RRL pipeline)

Cone search capability for table J/A+A/674/A17/table6 (Reclassification of 1160 objects incorrectly classified by the SOS Cep&RRL pipeline)

Cone search capability for table J/A+A/674/A17/table9 (List of sources for which the SOS Cep&RRL pipeline provides a metallicity estimate which should not be used as these stars are not Classical Cepheid pulsators)

Cone search capability for table J/A+A/674/A17/table10 (Association of Cepheids in the All Sky sample with open/globular clusters and with dwarf galaxies which are satellites of the Milky Way)

Cone search capability for table J/A+A/674/A17/table11 (Potential contaminants of type other than Cepheids)