Solute-coupled water transport and isotonic transport are basic functions of low- and high-resistance epithelia. These functions are studied with the epithelium bathed on the two sides with physiological saline of similar composition. Hence, at transepithelial equilibrium water enters the epithelial cells from both sides, and with the reflection coefficient of tight junction being larger than that of the interspace basement membrane, all of the water leaves the epithelium through the interspace basement membrane. The common design of transporting epithelia leads to the theory that an osmotic coupling of water absorption to ion flow is energized by lateral Na⁺/K⁺ pumps. We show that the theory accounts quantitatively for steady- and time dependent states of solute-coupled fluid uptake by toad skin epithelium. Our experimental results exclude definitively three alternative theories of epithelial solute-water coupling: stoichiometric coupling at the molecular level by transport proteins like SGLT1, electro-osmosis and a 'junctional fluid transfer mechanism'. Convection-diffusion out of the lateral space constitutes the fundamental problem of isotonic transport by making the emerging fluid hypertonic relative to the fluid in the lateral intercellular space. In the Na⁺ recirculation theory the 'surplus of solutes' is returned to the lateral space via the cells energized by the lateral Na⁺/K⁺ pumps. We show that this theory accounts quantitatively for isotonic and hypotonic transport at transepithelial osmotic equilibrium as observed in toad skin epithelium in vitro. Our conclusions are further developed for discussing their application to solute-solvent coupling in other vertebrate epithelia such as small intestine, proximal tubule of glomerular kidney and gallbladder. Evidence is discussed that the Na⁺ recirculation theory is not irreconcilable with the wide range of metabolic cost of Na⁺ transport observed in fluid-transporting epithelia.