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. Given its extreme astrometric accuracy and the repeated observations over five years, the observation modelling is done in a fully relativistic framework and several tests of General Relativity or of its extensions can be carried out during the data processing. The paper presents an overview of the current activities in this area and of the expected performances.