Neutron-induced cross sections represent the main nuclear input to models of stellar and Big-Bang nucleosynthesis. While (n,γ) reactions are relevant for the formation of elements heavier than iron, (n,p) and (n,α) reactions can play an important role in specific cases. The time-of-flight method is routinely used at n_TOF to experimentally determine the cross section data. In addition, recent upgrades of the facility will allow the use of activation techniques as well, possibly opening the way to a systematic study of neutron interaction with radioactive isotopes. In the last 20 years n_TOF has provided a large amount of experimental data for Nuclear Astrophysics. Our plan is to carry on challenging measurements and produce nuclear data in the next decades as well.