Ion-exchange membranes (IEMs) are increasingly used in dialysis and electrodialysis processes for the extraction, fractionation and concentration of valuable components, as well as reagent-free control of liquid media pH in the food industry. Fouling of IEMs is specific compared to that observed in the case of reverse or direct osmosis, ultrafiltration, microfiltration, and other membrane processes. This specificity is determined by the high concentration of fixed groups in IEMs, as well as by the phenomena inherent only in electromembrane processes, i.e., induced by an electric field. This review analyzes modern scientific publications on the effect of foulants (mainly typical for the dairy, wine and fruit juice industries) on the structural, transport, mass transfer, and electrochemical characteristics of cation-exchange and anion-exchange membranes. The relationship between the nature of the foulant and the structure, physicochemical, transport properties and behavior of ion-exchange membranes in an electric field is analyzed using experimental data (ion exchange capacity, water content, conductivity, diffusion permeability, limiting current density, water splitting, electroconvection, etc.) and modern mathematical models. The implications of traditional chemical cleaning are taken into account in this analysis and modern non-destructive membrane cleaning methods are discussed. Finally, challenges for the near future were identified.