In addition to its promising potential for applications, GaV4S8 shows very interesting physical properties with temperature and magnetic field. These properties can be tuned by applying hydrostatic pressure in order to reveal and understand the physics of these materials. Not only pressure induces an insulator-to-metal transition in GaV4S8 but it also has an interesting effect on the structural and magnetic transitions. Using a combination of AC calorimetry, capacitance, and resistivity measurements under pressure, we determine the evolution of the structural and magnetic transitions with pressure and thus establish the T-P phase diagram of GaV4S8. To detect the insulator-to-metal transition, we use optical conductivity and DC resistivity measurements and we follow the evolution of the Mott gap under pressure. The structural transition temperature increases with pressure and a second transition appears above 6 GPa indicating a possible new phase with a very small gap. Pressure has surprisingly a very weak effect on the ferromagnetic transition that persists even very close to the IMT that occurs at around 14 GPa, implying that the metallic state may also be magnetic.