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The ESA Gaia mission provides a unique time-domain survey for more than onebillion sources brighter than G=20.7 mag. Gaia offers the unprecedentedopportunity to study variability phenomena in the Universe thanks tomulti-epoch G-magnitude photometry in addition to astrometry, blue and redspectro-photometry, and spectroscopy. Within the Gaia Consortium, CoordinationUnit 7 has the responsibility to detect variable objects, classify them, derivecharacteristic parameters for specific variability classes, and provide globaldescriptions of variable phenomena.  We describe the variability processing and analysis that we plan to apply tothe successive data releases, and we present its application to the G-bandphotometry results of the first 14 months of Gaia operations that comprises 28days of Ecliptic Pole Scanning Law and 13 months of Nominal Scanning Law.  Out of the 694 million, all-sky, sources that have calibrated G-bandphotometry in this first stage of the mission, about 2.3 million sources thathave at least 20 observations are located within 38 degrees from the SouthEcliptic Pole. We detect about 14% of them as variable candidates, among whichthe automated classification identified 9347 Cepheid and RR Lyrae candidates.Additional visual inspections and selection criteria led to the publication of3194 Cepheid and RR Lyrae stars, described in Clementini et al. (2016). Underthe restrictive conditions for DR1, the completenesses of Cepheids and RR Lyraestars are estimated at 67% and 58%, respectively, numbers that willsignificantly increase with subsequent Gaia data releases.  Data processing within the Gaia Consortium is iterative, the quality of thedata and the results being improved at each iteration. The results presented inthis article show a glimpse of the exceptional harvest that is to be expectedfrom the Gaia mission for variability phenomena. [abridged]

Gaia Data Release 1: The variability processing & analysis and its application to the south ecliptic pole region