Astrometric tests of General Relativity in the Solar System: mathematical and computational scenarios

We review the mathematical models available for relativistic astrometry, discussing the different approaches and their accuracies in the context of the modern experiments from space like Gaia and GAME, and we show how these models can be applied to the real world, and their consequences from the mathematical and numerical point of view, with specific reference to the case of Gaia, whose launch is due before the end of the year.