Rapid plasma formation and evolution during highpower microwave (HPM) air breakdown in an HPM device produce a macroscopic plasma shield to the microwave transmission, which can severely limit the performance of the device. In this paper, the electromagnetic (EM)-plasma interaction and the HPM breakdown in air are modeled by a nonlinearly coupled full-wave Maxwell and plasma fluid system under conditions of high pressure and high collision frequency. The resulting multiphysics and multiscale system is solved by a nodal discontinuous Galerkin timedomain (DGTD) method, which is uniformly high order in both space and time. To demonstrate the capability of the DGTD method in the modeling of the HPM breakdown problems, the air breakdown and plasma formation in a metallic aperture are simulated, from which the underlining physical process can be interpreted and better understood.Index Terms-Air breakdown, discontinuous Galerkin time domain (DGTD), high-power microwave (HPM), nonlinear modeling, plasma fluid model, plasma formation, plasma shielding.