Extreme ultraviolet (EUV) lithographic tool is the core equipment to promote the development of integrated circuits to advanced technology nodes, and has been introduced into high volume manufacturing (HVM) of 7 nm technology node chips and below. High imaging quality is the basis of the application of the EUV lithography for HVM. As an important component of the EUV lithography imaging system, mask is a critical factor that affects the imaging quality. Mask defects, especially multilayer defects, are embedded in the EUV mask during the manufacturing process and result in the degradation of the imaging quality. To assure the imaging quality of EUV lithography, it is important to obtain the location, size, and profile of the mask defect accurately by inspection and compensate for the mask defects according to the information of them. Fast and accurate models for defective mask can help to compensate for the degradation of the imaging quality resulting from the mask defects effectively. In this paper, combining with the research work of our group in the field of mask defect inspection and defect compensation, the typical defective mask simulation methods are introduced, the existing mask inspection techniques are summarized, and the research progress of mask defect compensation techniques are introduced.