Extensional flow has been studied extensively for less than half the lifetime of the word “rheology”, although measurement of viscosity from extensional flow experiments can be traced back to the beginning of this century. In recent years extensional flow has, however, attracted a great deal of attention in conferences, workshops and special issues of journals. This has coincided with interest, both scientific and industrial, in elasticoviscous fluids, notably polymer solutions and molten polymers. The particular success of specialized, carefully targetted or focussed, workshops is highlighted. A personal reflection is offered here on some of the issues in extensional flow from the point of view of an applied mathematician. The state of the art, as far as extensional viscosity is concerned, is briefly surveyed. Both theoretical and practical aspects of the task of obtaining useful extensional flow properties are outlined, drawing heavily on a recent review by James and Walters. Particular attention is paid to spinning experiments, drawing heavily on recent theoretical investigations by the author. The merits of defining a “spinning viscosity”, in addition to the formally defined tensile viscosity, are advanced. The idea of general approximations for extensional flows is reviewed and some aspects of this are highlighted, particularly in connection with Metzner's idea of extensional primary field (EPF) approximations. Finally qualitative investigations of the behaviour of model fluids (in model flows) are illustrated and a new result on the boundedness of solutions for unsteady uniaxial extension of a FENS-P dumbbell model is presented.