Experimental results on the interaction of neutrons with intermediate and heavy nuclei are summarized. Until recently the interaction of nucleons with nuclei has usually been described in terms of the compound nucleus theory. The data presented, however, can not be accounted for by the compound nucleus theory. It appears to be necessary to assume instead that a neutron can traverse a nucleus rather easily with only a small chance of being absorbed into a compound system. Feshbach, Porter, and Weisskopf have proposed an optical potential consisting of a complex square well to account for the experimental data. While this model gives better agreement with the experiments than the compound nucleus theory, it leads to some inconsistencies. In order to be consistent with the results of measurements on neutrons and with the shell model the potential needs to be modified to be deeper than that used by Feshbachet al., and it should contain a spin-orbit coupling term.