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Thin-film multilayer monochromators have been fabricated and studied by neutron diffraction. Alternating thin films of two materials, such as Mn and Ge, constitute a one-dimensional crystal owing to the contrast in their scattering amplitude densities. The following are novel features of such a monochromator: (1) large and adjustable d spacing, (2) very high reflectivity, (3) adjustable bandwidth, Δλ/λ. Both kinematical and dynamical theories have been developed to give a proper understanding of the properties of a multilayer. Since a deviation from perfect periodicity can have a substantial effect on diffraction properties of a multilayer, a 'disorder factor' has been introduced in the dynamical theory. Finite resolution of the spectrometer has been taken into consideration when the experimental data are compared with the theoretical expressions. These multilayers can also be used as excellent polarizers and filters for neutrons.