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Artificial charged membranes, similar to the biological membranes, are self-assembled nanostructured materials constructed from macromolecules. The mutual interactions of parts of macromolecules leads to phase separation and appearance of microheterogeneities within the membrane bulk. On the other hand, these interactions also cause spontaneous microheterogeneity on the membrane surface, to which macroheterogeneous structures can be added at the stage of membrane fabrication. Membrane bulk and surface heterogeneity affect essentially the properties and membrane performance in the applications in the field of separation (water desalination, salt concentration, food processing and other), energy production (fuel cells, reverse electrodialysis), chlorine-alkaline electrolysis, medicine and other. We review the models describing ion transport in ion-exchange membranes and electromembrane systems with an emphasis on the role of micro-and macroheterogeneities in and on the membranes. Irreversible thermodynamics approach, "solution-diffusion" and "pore-flow" models, the multiphase models built within the effective-medium approach are examined as the tools for describing ion transport in the membranes. 2D and 3D models involving or not convective transport in electrodialysis cells are presented and analysed. Some examples are given when specially designed surface heterogeneity on the membrane surface results in enhancement of ion transport in intensive current electrodialysis.Recently, Svoboda et al. [13] developed a specific scanning cell for the analysis of heterogeneous IEM structure by micro-computed tomography, which provides volume reconstruction of the studied material. The unique working principle of the cell allows one to scan membranes not only in their dry state but also in fully swollen state. The micro-computed tomography showed that there are profound changes in the structure of the IEM associated with their transition from the dry state into the swollen one. This study applied to the heterogeneous cation-exchange membrane (CEM) coming from Mega a.s., Czech Republic showed that swelling of the membrane is caused by the swelling of the ion-exchange resin. Its volume increased nearly three times after exposure to deionized water, while the overall membrane volume increased by 50%. If the membrane contained approximately 28%vol. of the resin in the dry state, this content increased to 52%vol. after swelling.Micro-computed tomography not only allows one to analyse volumetric composition of the membrane bulk but also to quantify the composition of the surface. By using two different methods, Vobecka et al. [14] evaluated the fraction of the conductive area (e.g., the ion-exchange resin) on the surface of an AEM and CEM in the swollen state. The obtained results showed that the volume fraction of the conductive domains does not correspond to the surface fraction of these domains and thus the volume composition is not reflected on their surface. For example, the volume fraction of the conductive domains for the st...

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