Abstract: Because the classical streamer discharge theory is difficult to explain the rapid breakdown of gas under nanosecond short pulse voltage, the runaway electron breakdown theory is proposed. In order to help understand the theory of runaway electron breakdown, this paper first gives a brief introduction of its development history, and then presents our PIC/MCC simulation results for nanosecond short pulse discharge in atmospheric air. Under negative polarity, with the increase of breakdown voltage, the evolution of runaway electrons from nothing was observed, and sufficient conditions for the generation of runaway electrons were proposed. The pre-ionization channel generated by runaway electron in front of discharge channel head was found and its important role in the rapid breakdown of air gap was indicated. The time required for the channel to cross the air gap under the positive and negative 26 kV breakdown voltage was compared, and the polarity effect reversal of the breakdown voltage was explained. It is found that the highest energy electrons only appear in the strong electric field area at the head of the discharge channel. Even if the electric field there exceeds the critical value, it is difficult for the electrons to enter the continuous acceleration mode. Therefore, the energy of the highest energy electrons is much smaller than that in the negative polarity. Finally, the contribution of high-energy electrons to the rapid breakdown of the air gap is pointed out.