The last 20 years have seen major advances in the understanding of the mechanisms and molecular bases of water transport across cell membranes. Prominent among these advances was the discovery of a family of transmembrane proteins that permeate exclusively or dominantly water (aquaporins), followed by structural studies identifying the intramolecular permeation pathway, as well as by studies directed to a detailed understanding of these molecules in health and disease. Agre and colleagues (Agre et al. 2002) discuss the molecular structure of aquaporins and the physiology and pathophysiology of aquaporins in diverse organs and tissues. Another important advance was the development of methods for rapid measurements of changes in cell volume. This resulted in accurate estimates of cell-membrane water permeability, and in the prediction that very small osmotic gradients would suffice to drive transepithelial transport, without the need for the existence of compartments of much higher osmolality than that of the bathing solution. Around 1990, faced with the question of what pathways and driving forces underlie net water fluxes across cell membranes, most physiologists working on animal cells would have had direct and clear answers. Water moves across the phospholipid moiety of the plasma membrane (although this membrane can be extremely water-tight in certain cases), and through water pores, in cells that express these proteins. The driving force is the difference in effective osmolality across the cell membrane. Enlightened physiologists working on epithelia would add that transepithelial water absorption or secretion is always a passive phenomenon, secondary to net solute transport in the same direction. Further, complicated compartment models, such as the standing osmotic gradient hypothesis, are unnecessary to explain water transport, because very small osmotic gradients, perhaps too small to measure directly, are a sufficient driving force. The question of how water fluxes are partitioned between transcellular and paracellular pathways remained difficult to answer because of the lack of direct measurements. The two central questions in the problem of water transport across simple or complex membranes are the pathway and the mechanism. Considering the cell membrane, one asks whether water permeates the lipid moiety and/or transmembrane proteins. These pathways are expected to have different properties, including the possibility that transmembrane water pores could also be permeable to other molecules. Concerning the driving force for water transport, in principle it could be primary active, secondary active or passive. At the time prior to the discoveries that provide the experimental bases for the Topical Reviews in this Special Issue, the virtually unanimous opinion of the experts would have been that water transport is passive. With respect to transepithelial water transport, the relative contributions of the transcellular and paracellular routes remain to be determined. There is no agreement on the molecular mechanism, i.e. whether there is secondary-active water transport at the cell membrane in addition to simple osmosis, or on the precise nature of osmotic water flow, i.e. is there truly isosmotic transport? This Special Issue highlights the current excitement in this area of physiology. Three current controversies in the field of water transport are discussed. In each case, the ‘controversial’ novel theory is presented (in the form of a Topical Review) and discussed critically in the form of a Perspective or a Research Paper. The three controversies presented in this Special Issue were debated at the XXXIV International Congress of Physiological Science in Christchurch, New Zealand.