Mixed powders of Bi2O3 and Fe2O3 are shown to yield single-phase, dense nanostructured polycrystals of BiFeO3 in reaction flash sintering experiments, carried out by applying a field of 50 V cm(-1) and with the current limit set to 35 mA mm(-2). The furnace was heated at a constant rate with the reaction sintering taking place abruptly upon reaching 625 degrees C. Remarkably, an intermediate bismuth-rich phase of the oxide that forms just before reaching the flash temperature transforms, and at the same time sinters, into singlephase BiFeO3 within a few seconds after the onset of the flash. The BiFeO3 so produced is electrically insulating, a property that is critical to its applications. This one-step synthesis of single-phase polycrystals of complex oxides from their basic constituents, by reaction flash sintering, is a significant development in the processing of complex oxides, which are normally difficult to sinter by conventional methods.