Many experimental and numerical studies have been conducted to elucidate the fascinating physics of plasma formation and shock wave propagation during millimeter wave beam irradiation outputted from a high averagepower gyrotron. A microwave-rocket system for rocket launching was proposed as an engineering application using an intense millimeter wave beam. Flight demonstrations and thrust measurements were repeated while changing the ambient pressure, beam power density, beam profile, and vehicle shape. We reviewed reports of experimental and computational studies to assess information on plasma propagation and compressible fluid dynamics induced by the millimeter wave beam. Earlier experiments and simulations of rocket launching were also examined for this study.