GaSe is a layered semiconductor with an optical band gap tunable by the number of layers in a thin film. This is promising for application in micro/optoelectronics and photovoltaics. However, for that, knowledge about the intrinsic defects are needed, since they may influence device behavior. Here we present a comprehensive study of intrinsic point defects in both bulk and monolayer (ML) GaSe, using an optimized hybrid functional which reproduces the band gap and is Koopmans' compliant. Formation energies and charge transition levels are calculated, the latter in good agreement with available experimental data. We find that the only intrinsic donor is the interlayer gallium interstitial, which is absent in the case of the ML. The vacancies are acceptors, the selenium interstitial is electrically inactive, and small intrinsic defect complexes have formation energies too high to play a role in the electronic properties of samples grown under quasi-equilibrium conditions. Bulk GaSe is well compensated by the intrinsic defects, and is an ideal substrate. The ML is intrinsically p-type, and p-type doping cannot be compensated either. The opening of the band gap changes the defect physics considerably with respect to the bulk.