Gaia is an ambitious space astrometry mission of ESA with a main objective to map the sky in astrometry and photometry down to a magnitude 20 by the end of the next decade. While the mission is built and operated by ESA and an industrial consortium, the data processing is entrusted to a consortium formed by the scientific community, which was formed in 2006 and formally selected by ESA one year later. The satellite will downlink around 100 TB of raw telemetry data over a mission duration of 5 years from which a very complex iterative processing will lead to the final science output: astrometry with a final accuracy of a few tens of microarcseconds, epoch photometry in wide and narrow bands, radial velocity and spectra for the stars brighter than 17 mag. We discuss the general principles and main difficulties of this very large data processing and present the organization of the European Consortium responsible for its design and implementation.