The water flow across porous, semipermeable membranes associated with osmosis and filtration under a variety of conditions is analysed and compared to macromolecular diffusion across free-liquid boundaries, diffusion and sedimentation in the ultracentrifuge, and tracer diffusion of water. This study establishes that osmosis can be explained in terms of the irreversible thermodynamics of diffusion. For macromolecular osmotically active solutes in the semidilute concentration regime the water flows across semipermeable porous membranes are interpreted in terms of a rate-limiting solute-solvent exchange layer that exists on the solution side of the membrane adjacent to the membrane pore; both osmosis and filtration will be governed by these exchange layers. These exchange layers also yield unique properties of their constituent molecules in systems where there is osmotic equilibration between solutions of different solutes. This study also establishes the need to consider the internal osmotic pressure of membranes in the pressure balance associated with the flow across the membrane. The complex situation of partially permeable membranes is analysed for the simple case where there are no mechanical gradients and there is only one osmotically active solution that creates a rate-limiting exchange layer. This treatment predicts that the flow will be governed primarily by the osmotic pressure difference associated with the partitioning of the solute at the membrane-solution interface.