The phenomenon of phase transitions in one-dimensional systems is discussed. Equilibrium systems are reviewed and some properties of an energy function which m a y allow phase transitions and phase ordering in one dimension are identi ed. We then give a n o verview of the one-dimensional phase transitions which h a ve been studied in nonequilibrium systems. A particularly simple model, the zero-range process, for which the steady state is known exactly as a product measure, is discussed in some detail. Generalisations of the model, for which a product measure still holds, are also discussed. We analyse in detail a condensation phase transition in the model and show h o w conditions under which i t m a y occur may be related to the existence of an e ective long-range energy function. It is also shown that even when the conditions for condensation are not ful lled one can still observe v ery sharp crossover behaviour and apparent condensation in a nite system. Although the zero-range process is not well known within the physics community, several nonequilibrium models have been proposed that are examples of a zero-range process, or closely related to it, and we review these applications here.