This review of the high-speed breakdown ionization waves is based on the recent theoretical and experimental investigations of the gas breakdown by high voltage pulse with nanosecond rise time. The governed parameters of these breakdown ionization waves are summarized and analyzed, The attention is mainly focused on the breakdown ionization waves with extremely high propagation velocities belong to the sublight range 10(9) - 2 . 10(10) cm s-1, that released at the amplitude of applied voltage pulses of 20-300 kV. At gas pressures less than hundred torrs the reduced electric field strength in the front of the breakdown ionization wave is too high, that this region becomes an intensive movable source of the high energy electrons with typical current exceeds several kA. Theese high energy electrons propagate with the velocity more than that of the breakdown ionization waves and provide initial ionization before it. At pressures less than several torrs these electrons play a key role in the breakdown ionization wave propagation. At high pressure above 200 torrs the radiation from the breakdown ionization wave front has a key role at gas preionization. A high speed fulfillment of the gas gap by strongly excited non equilibrium cold plasma released at the breakdown ionization wave propagation, high electric field strenght in its front, high currents of generated energetic electrons etc. are interesting from physical point of view and provide the remarkable opportunities for various scientific and technological applications.