NASA OSIRIS-REx and JAXA Hayabusa 2 sample-return missions have targeted two near-Earth asteroids: (101955) Bennu and (162173) 1999 JU3, respectively. These are primitive asteroids that are believed to originate in the inner belt, where five distinct sources have been identified: four primitive collisional families (Polana, Erigone, Sulamitis, and Clarissa), and a population of low-albedo and low-inclination background asteroids. Identifying and characterizing the populations from which these two NEAs might originate will enchance the science return of the two missions.With this main objective in mind, we initiated in 2010 a spectroscopic survey in the visible and the near-infrared to characterize the primitive collisional families in the inner belt and the low-albedo background population. This is the PRIMitive Asteroids Spectroscopic Survey – PRIMASS. So far we have obtained more than 200 spectra using telescopes located at different observatories. PRIMASS uses a variety of ground based facilities. Most of the spectra have been obtained using the 10.4m Gran Telescopio Canarias (GTC), and the 3.6m Telescopio Nazionale Galileo (TNG), both located at the El Roque de los Muchachos Observatory (La Palma, Spain), and the 3.0m NASA Infrared Telescope Facility on Mauna Kea (Hawai, USA).We present the first results from our on-going survey (de Leon et al. 2015; Pinilla-Alonso et al. 2015; Morate et al. 2015), focused on the Polana and the Erigone primitive families, with visible and near-infrared spectra of more than 200 objects, most of them with no previous spectroscopic data. Our survey is already the largest database of primitive asteroids spectra, and we keep obtaining data on the Sulamitis and the Clarissa families, as well as on the background low-albedo population.