The use of neutron spectroscopy to study the properties of nuclei is reviewed. The development of neutron spectroscopy over the years and the principal results are discussed briefly. The experimental methods of neutron spectroscopy are described. Emphasis is placed on the new directions in neutron spectroscopy of nuclei: the alpha decay of compound states excited during neutron capture by nuclei, hyperfine interactions in neutron resonances, and the properties of few-nucleon nuclei in reactions with neutrons. The most important experimental results are discussed and compared with the theory.