Mask inspection is essential for the success of any pattern-transfer lithography technology, and EUV Lithography in particular faces unique challenges. EUV masks resonant-reflective multilayer coatings have a narrow, wavelength-specific response that dramatically affects the way that defects appear, or disappear, at various illuminating wavelengths. Furthermore, the ever-shrinking size of 'critical' defects limits the potential effectiveness of DUV inspection techniques over time. Researchers pursuing numerous ways of finding and characterizing defects on EUV masks and have met with varying degrees of success. Their lessons inform the current, urgent exploration to select the most effective techniques for high-volume manufacturing. Ranging from basic research and demonstration experiments to commercial inspection tool prototypes, we survey the recent history of work in this area, including sixteen projects in Europe, Asia, and America. Solutions range from scanning beams to microscopy, dark field imaging to pattern transfer.