Just over a century ago, Smoluchowski derived his celebrated formula for the electrokinetic slip velocity, which handles both the electrophoresis of colloids and electro-osmotic flows over solid surfaces under a range of conditions. Here we discuss interesting and surprising effects that arise with electrokinetics over liquid-liquid interfaces. A central observation is that the (strong) shear rates that arise in electro-osmosis can drive liquid/liquid interfaces to flow, unlike their solid/liquid counterparts, and thus enhance electrokinetic velocities, potentially by orders of magnitude. We pay particular attention to the electrophoretic mobility of liquid drops, which has been the subject of over a half-century's debate. Levich and Frumkin argued via electrocapillarity that the electrophoretic mobility of a charged mercury drop should significantly exceed that of a similarly-charged solid particle. By contrast, the more conventional electrokinetic calculation by Booth revealed no such enhancement. In the decades since, various efforts have been made to resolve this discrepancy, reconcile the two pictures and delineate the conditions under which this dramatic enhancement should occur. We present a clear physical picture for the mechanism behind this dramatic increase in mobility, provide an intuitive sense for when and why such increases can be expected, and discuss implications and adaptations for microfliudic systems.