A systematic review is given of the various approaches to the theory of molecular flow in the interior of vessels and of molecular effusion into vacuum. The approximate character of the photometric model, widely used at present in effusion calculations, is noted. It is shown that effusion is determined by three factors: 1) kinetics of chemical reactions involving molecular fluxes on the walls of vessels; 2) local kinematics of the reflection of these fluxes by the walls, and 3) shape of the vessel and of the effusion aperture. A detailed analysis is given of each of these factors from both experimental and theoretical standpoints. Attention is drawn to possible applications of neutron-transport theory, and a number of geometric probability theorems, to the effusion problem. Possible, desirable, and essential topics for future theoretical and experimental research into effusion are enumerated. The literature cited covers the period essentially up to the end of 1974.