For about 60 years, it is known that "limiting current" density does not really limit the current density in electrodialysis (ED). The use of intensive currents allows one to decrease the area of expensive ion-exchange membranes, hence to obtain more compact ED plants with lower investment costs. However, in practice overlimiting currents are applied solely in electrodeionization, and not in conventional ED devices. In literature (H. Strathmann [1]), overlimiting current density operation ED is considered as being under ongoing research and development. Where is the research today? What is the actual understanding of overlimiting mass transfer processes in membrane systems? As far as electroconvection is involved as a major mechanism of overlimiting transfer, what could bring specific knowledge and practice acquired in nano- and microfluidics into desalination? Can overlimiting ED be economically advantageous? Is there an altemative for classical ED devices applied? This review is intended to give some responses to these questions. (C) 2014 Elsevier B.V. All rights reserved.