An important experimental program on Nuclear Astrophysics is being carried out at the n-TOF since several years, in order to address the still open issues in stellar and primordial nucleosynthesis. Several neutron capture reactions relevant to s-process nucleosynthesis have been measured so far, some of which on important branching point radioisotopes. Furthermore, the construction of a second experimental area has recently opened the way to challenging measurements of (n, charged particle) reactions on isotopes of short half-life. The Nuclear Astrophysics program of the n-TOF Collaboration is here described, with emphasis on recent results relevant for stellar nucleosynthesis, stellar neutron sources and primordial nucleosynthesis. © The Authors, published by EDP Sciences, 2017.