In this work our ability to understand thermal-neutron spectra in graphite-moderated reactor systems is examined on the basis of a theoretical description of neutron scattering that begins at the microscopic level. The first step in this examination consists in determining the extent to which current ideas of lattice vibrations in graphite are consistent with measurements of the scattering law and of specific heats. Theoretical scattering laws and specific heats based on a few different models for lattice vibrations are compared with experimental results. The theoretical scattering law is calculated within the framework of the incoherent and Gaussian approximations. The question of the accuracy of the latter approximation is discussed in detail. No estimates have been made of the magnitude of the uncertainty introduced by the use of the incoherent approximation. Following the discussion of neutron scattering at the microscopic level, we show (1) the sensitivity of various integral properties of the scattering kernel and of thermal-neutron spectra in a homogeneous medium to the frequency distribution of lattice vibrations, and (2) the accuracy of the Gaussian approximation for use in computing thermal-neutron spectra in graphite. Finally, a detailed theoretical model for the scattering of neutrons by graphite is applied to the problem of comparing calculated neutron spectra with the measured spectra in two strongly heterogeneous, graphite-moderated assemblies. These considerations show that current theoretical ideas concerning the frequency distribution of lattice vibrations in graphite are consistent with the results of the measurement of the scattering law, with the specific heat, and with most of the available results of the measurements of thermal-neutron spectra in reactor-like configurations.