Two Neutral Beam Injectors (NBI) are foreseen to provide a substantial fraction of the heating power necessary to ignite thermonuclear fusion reactions in ITER. The development of the NBI system at unprecedented parameters (40 A of negative ion current accelerated up to 1 MV) requires the realization of a full scale prototype, to be tested and optimized at the Test Facility under construction in Padova (Italy). The beam source is the key component of the system and the design of the multi-grid accelerator is the goal of a multi-national collaborative effort. In particular, beam steering is a challenging aspect, being a tradeoff between requirements of the optics and real grids with finite thickness and thermo-mechanical constraints due to the cooling needs and the presence of permanent magnets. In the paper, a review of the accelerator physics and an overview of the whole R&D physics program aimed to the development of the injector source are presented.