The study of the resonant structures in neutron-nucleus cross-sections, and therefore of the compound-nucleus reaction mechanism, requires spectroscopic measurements to determine with high accuracy the energy of the neutron interacting with the material under study. To this purpose, the neutron time-of-flight facility n_TOF has been operating since 2001 at CERN. Its characteristics, such as the high intensity instantaneous neutron flux, the wide energy range from thermal to few GeV, and the very good energy resolution, are perfectly suited to perform high-quality measurements of neutron-induced reaction cross sections. The precise and accurate knowledge of these cross sections plays a fundamental role in nuclear technologies, nuclear astrophysics and nuclear physics. Two different measuring stations are available at the n_TOF facility, called EAR1 and EAR2, with different characteristics of intensity of the neutron flux and energy resolution. These experimental areas, combined with advanced detection systems lead to a great flexibility in performing challenging measurement of high precision and accuracy, and allow the investigation isotopes with very low cross sections, or available only in small quantities, or with very high specific activity. The characteristics and performances of the two experimental areas of the n_TOF facility will be presented, together with the most important measurements performed to date and their physics case. In addition, the significant upcoming measurements will be introduced.