  Context. Gaia has been in operations since 2014. The third Gaia data release
expands from the early data release (EDR3) in 2020 by providing 34 months of
multi-epoch observations that allowed us to probe, characterise and classify
systematically celestial variable phenomena.
  Aims. We present a summary of the variability processing and analysis of the
photometric and spectroscopic time series of 1.8 billion sources done for Gaia
DR3.
  Methods. We used statistical and Machine Learning methods to characterise and
classify the variable sources. Training sets were built from a global revision
of major published variable star catalogues. For a subset of classes, specific
detailed studies were conducted to confirm their class membership and to derive
parameters that are adapted to the peculiarity of the considered class.
  Results. In total, 10.5 million objects are identified as variable in Gaia
DR3 and have associated time series in G, GBP, and GRP and, in some cases,
radial velocity time series. The DR3 variable sources subdivide into 9.5
million variable stars and 1 million Active Galactic Nuclei/Quasars. In
addition, supervised classification identified 2.5 million galaxies thanks to
spurious variability induced by the extent of these objects. The variability
analysis output in the DR3 archive amounts to 17 tables containing a total of
365 parameters. We publish 35 types and sub-types of variable objects. For 11
variable types, additional specific object parameters are published. An
overview of the estimated completeness and contamination of most variability
classes is provided.
  Conclusions. Thanks to Gaia we present the largest whole-sky variability
analysis based on coherent photometric, astrometric, and spectroscopic data.
Later Gaia data releases will more than double the span of time series and the
number of observations, thus allowing for an even richer catalogue in the
future.
