Keywords: Extended Space Charge, Concentration Polarization, Overlimiting Conductance, Nonequilibrium Electroosmotic Instability Abstract: Our talk is about ionic currents from an electrolyte solution into a charge selective solid, such as, an electrode, an ion exchange membrane or an array of nano-channels in a micro-fluidic system, and the related viscous fluid flows on the length scales varying from nanometers to millimeters. All systems of this kind have characteristic voltage-current curves with segments in which current nearly saturates at some plateau values due to concentration polarization – formation of solute concentration gradients under the passage of a DC current. We start by reviewing a few seemingly different phenomena occurring in that range. These are anomalous rectification in cathodic copper deposition from a copper sulfate solution, super-fast vortexes near an ion-exchange granule, over-limiting conductance in electrodialysis and the recently observed non equilibrium electroosmotic instability. All these phenomena result from formation of an additional extended space charge layer next to that of a classical electric double layer at the solid/liquid interface. We review the peculiar features the extended space charge and their relation to the mechanisms of the above mentioned phenomena.