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.