Weakly conducting dielectric solid particles and liquid droplets in strong electric fields are known to undergo symmetry-breaking bifurcations leading to steady electrorotation. This so-called Quincke effect, which results from the antiparallel electrostatic dipole induced by the applied field inside the particles, is well described by the classic Taylor-Melcher leaky dielectric model. In this talk, I will discuss consequences of the Quincke effect on the dynamics of deformable liquid drops, which we analyze numerically using a novel three-dimensional boundary-element formulation. Unlike previous studies that have neglected interfacial charge transport or assumed axisymmetric shapes, our simulations include nonlinear charge convection by the fluid flow and are the first to capture the three-dimensional transition to electrorotation. Our numerical results show excellent agreement with existing experimental data and with an improved small deformation theory. They also reveal the existence of interfacial charge shocks in low viscosity drops, for which we also propose a simple theoretical model. Recent results on Quincke electrorotation in suspensions of electrohydrodynamically interacting particles will also be discussed.