We briefly review the historical and modern relationship between the measurements of stellar positions and the spacetime modelling. The emphasis is put on modern space astrometry, more specifically the ESA missions Hipparcos and Gaia, given the extreme accuracy reached in global astrometry in space. We outline the relativistic modelling for missions like Gaia and SIM and show the importance of having a consistent relativistic approach all the way through the data analysis. In the last parts of the paper we hint on the impact of a mission like Gaia to test several predictions of General Relativity much beyond the current level and the way Gaia will set up a practical realisation of the inertial frame in the visible wavelengths.