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The third Gaia Data Release, covering 34 months of data, includes the secondGaia catalogue of long-period variables (LPVs), with G variability amplitudeslarger than 0.1 mag (5-95% quantile range). The paper describes the productionand content of this catalogue, and the methods used to compute the publishedvariability parameters and identify C-star candidates. We applied variousfiltering criteria to minimise contamination by other kinds of variables. Thevariability parameters, period and amplitude, were derived from model fits tothe G-band light curves, wherever possible. C stars were identified using theirmolecular signature in the low-resolution RP spectra. The catalogue contains 1720 558 LPV candidates, including 392 240 stars with published periods (rangingfrom 35 to1000 days) and 546 468 stars classified as C-stars candidates.Comparison with literature data (OGLE and ASAS-SN) leads to an estimated 80% ofcompleteness. The recovery rate is about 90% for the most regular stars(typically Miras) and 60% for semi-regular and irregular ones. At the sametime, the number of known LPVs is increased by a large factor with respect tothe literature data, especially in crowded regions, and the contamination isestimated to be below two percents. Our C-star classification, based on solidtheoretical arguments, is consistent with spectroscopically identified C starsin the literature. Caution must however be taken if the S/N ratio is small, incrowded regions or if the source is reddened by some kind of extinction. Thequality and potential of the catalogue are illustrated by presenting anddiscussing LPVs in the solar neighbourhood, in globular clusters and ingalaxies of the Local Group. This is the largest all-sky catalogue of LPVs todate with a photometric depth down to G=20 mag, providing a unique data set forresearch on late stages of stellar evolution.

Gaia Data Release 3: The second Gaia catalogue of Long-Period Variable candidates