Gaia is an ESA space mission launched on 19 December 2013 with the main goal to provide astrometric and spectro-photometric measurements of over one billion celestial objects. The accuracy of the astrometric parameters at the end of the mission (at least 5 years of observations) should reach the level of about 10 microarcseconds for stars of optimal brightness. This level of accuracy allows one to realize a bundle of relativistic tests in the weak-field regime of the solar system as well as to provide a number of results relevant for strong-field tests of general relativity. An overview of Gaia modelling and results is provided here with the emphasis on the complications that one faces when measuring the PPN parameter γ using space astrometry mission like Gaia.