SaToR-G (Satellites Tests of Relativistic Gravity) is a new experiment of gravitation that aims to test the gravitational interaction beyond the predictions of General Relativity (GR) in search for effects foreseen by other alternative theories of gravitation and possibly connected with “new physics”. SaToR-G is financed by the Astroparticle Physics Experiments of the Italian “Istituto Nazionale di Fisica Nucleare” (INFN) and takes advantage of the improved dynamical model of the two LAGEOS laser-ranged satellites and of the LARES one achieved within the previous experiment LARASE (LAser RAnged Satellites Experiment). The improvements mainly concern the modeling of the non-conservative forces (NCF) acting on the surface of the satellites considered and that of the Earth's gravitational field during their precise orbit determination (POD). Regarding the NCF, the main efforts were in the development of a model for the spin of the satellites (LASSOS: LArase Satellites Spin mOdel Solutions) and a model for thermal thrust forces (LATOS: LArase Thermal mOdel Solutions). For the gravitational field, the monthly solutions of the GRACE mission have been implemented in the code used for the POD. After a summary of the main results obtained by LARASE in the field of gravitation the main objectives of SaToR-G and the planned strategy for achieving them will be presented.