Transport from the liquid phase through homogeneous polymeric membranes has several features that distinguish it from gas and vapour permeation. The concentration of permeant in the polymer is usually high and has a large influence on diffusion coefficients. The driving force for transport, the gradient of chemical potential of the liquid, may be controlled by the application of a pressure but the functional form of the dependence of chemical potential on pressure is different in a liquid from that which applies in gas diffusion. Frequently the chemical potential gradients in liquid transport are small. ‐ The driving force may also be controlled by varying the composition of the liquid phases i. e. by setting up an osmotic pressure difference across the membrane. This can only be done with systems of more than one component and the study of transport from the liquid phase therefore leads readily into the study of several simultaneous fluxes and the possibilities of membrane selectivity and separation. ‐ This paper reviews work on the mechanisms of steady flow of, principally, organic liquids through polymer membranes under pressure from the liquid phase into either another liquid phase, as in hyperfiltration, or into a vapour phase as in pervaporation. The transport of a single liquid is considered first Then the flow of binary liquid mixtures is discussed and the mechanisms of separations or organic liquids by hyperfiltration and pervaporation are examined.