We investigate the microscopic mechanisms responsible for microdomain alignment in block copolymer solutions exposed to an electric field. Using time-resolved synchrotron small-angle x-ray scattering, we reveal two distinct processes, i.e., grain boundary migration and rotation of entire grains, as the two dominant microscopic mechanisms. The former dominates in weakly segregating systems, while the latter is predominant in strongly segregated systems. The kinetics of the processes are followed as a function of polymer concentration and temperature and are correlated to the solution viscosity.