Neutrons are a principal tool for the study of lattice vibrational spectra in materials. This article provides a detailed account of fission and spallation methods of neutron production that are capable of producing sufficient intensity to be useful in neutron scattering research. It describes the instrumentation required for, and advancements made in, neutron powder diffraction. The article further explains the texture and residual stress (macrostresses and microstresses) problems that are analyzed using the neutron powder diffraction method. It also outlines the single-crystal neutron diffraction technique, and provides examples of the applications of neutron diffraction.