Abstract: The paper reviews the worldwide research status and progress of dielectric window (DW) breakdown in vacuum under high power microwave (HPM). With respect to experimental studies, representative research results aboard are introduced, and the laws of breakdown development on the DW surface and inside the DW and the corresponding theoretical model are presented according to the results introduced combined with our research. With respect to theory and simulation studies, the progress aboard in understanding the mechanism of DW surface multipactor discharge under HPM is discussed, which is achieved with Monte Carlo and particle-in-cell simulations. Then along with our research, motion laws of DW surface electrons with diffe-rent emission angles and microwave electromagnetic parameters are introduced, and another theoretical model is proposed, which can essentially explain why the multipactor electron number and the surface electrostatic field oscillate at a frequency twice that of the HPM. Finally, several effective DW breakdown suppression technologies are summarized.