General Relativity (GR) has never been the only theory claiming to provide a detailed description of the gravitational interaction beyond the Newtonian limit. Although GR is still the most favoured alternative, either because of the experimental results or of its simplicity, several other theories have been proposed. The large number of theoretical alternatives naturally called for experimental verifications and for mathematical tools able to ease their interpretation. In regard of the former, it is well known that the first experimental evidences in support of GR came from astrometry. This technique became less competitive during the years, but it is making a comeback thanks to the Gaia mission and to other related astrometric experiments and proposed missions. Here it will be given a brief summary of the astrometric tests of gravity theories that are planned and/or under study, and of their motivations and theoretical context.