point-like ions in chemical equilibrium with a surface whose

double-layer voltage is of order the thermal voltage, $kT/e = 25$

mV. In nonlinear electrokinetic phenomena, such as AC

electro-osmosis and induced-charge electrophoresis, several Volts

$\approx 100\, kT/e$ are applied to the double layer, so the theory

breaks down and cannot explain many observed features. In this

paper, we review the relevant literature and argue that, under such

a large voltage, counterions condense near the surface, even for

dilute bulk solutions, and the classical concepts of ``compact

layer'' and ``shear plane'' must be generalized. Using simple

continuum models, we predict (at least) two basic trends at large

voltages: (i) the growth of a condensed layer decreases the

double-layer differential capacitance, and (ii) viscosity increase

with counterion condensation reduces the electro-osmotic

mobility. The former may explain observed flow reversal in AC

electro-osmotic pumps, while the latter may explain the decay of all

induce-charge electro-osmotic phenomena at high salt concentration,

although a complete theory is still lacking. Through several

colloidal examples, such as the electrophoresis of an uncharged

metal sphere in an asymmetric electrolyte, we predict that induced

electro-osmotic flows are generally ion-specific at large voltages,

even in the absence of Faradaic reactions.