The present review, containing 178 references, is dedicated to one of the largest and most important branches of the rarefied gas dynamics, namely internal flows. A critical analysis of the corresponding numerical data and analytical results available in the literature was made. The most reliable data were selected and tabulated. The review will be useful as a reference for mathematicians, physicists and aerodynamicists interested in rarefied gas flows. In this paper the complete ranges of the main parameters, determining rarefied gas flows through a capillary, are covered. The capillary length varies from zero, when the capillary degenerates into a thin orifice, to infinity when the end effects can be neglected. The Knudsen number, characterizing the gas rarefaction, varies from zero when the gas is considered as a continuous medium to infinity when the intermolecular collisions can be discounted. The pressure and temperature drops on the capillary ends vary from the small values when the linear theory is valid to the large values when the nonlinear equations must be applied. The influence of the gas–surface interaction is considered.