We investigate the microdomain orientation kinetics of concentrated block copolymer solutions exposed to a dc electric field by time-resolved synchrotron small-angle X-ray scattering. As a model system, we use a lamellar polystyrene-b-polyisoprene block copolymer dissolved in toluene. Our results indicate two different microscopic mechanisms, i.e., nucleation and growth of domains and grain rotation. The former dominates close to the order-disorder transition, while the latter prevails under more strongly segregated conditions. This conclusion is corroborated by computer simulations based on dynamic density functional theory. The orientation kinetics follows a single-exponential behavior with characteristic time constants varying from a few seconds to some minutes depending on polymer concentration. temperature, and electric field strength. From the experimental results we deduce optimum conditions for the preparation of highly anisotropic bulk polymer samples via solvent casting in the presence of an electric field.