Microfluidics has rekindled interest in electrokinetics, the study of electrically driven fluid flow past charged surfaces (“electro-osmosis”) and the related motion of charged particles (“electrophoresis”), due to favorable scaling with miniaturization. Classical electrokinetic phenomena are linear in the applied voltage, due the assumption of fixed surface charge, but a much richer class of nonlinear electrokinetic phenomena can occur around polarizable surfaces, where an electric field acts on its own induced charge. This lecture presents the basic physics of “induced-charge electro-osmosis” and describes some engineering applications. Examples include microfluidic pumping by an electro-osmotic “fluid conveyor belt,” and transverse electrophoresis of metal/dielectric Janus particles in AC fields. These remarkable phenomena also raise fundamental questions about electrokinetics at large induced voltages, leading to new mathematical models accounting for the crowding of ions against highly charged surfaces.