Photomask repair is a process of editing local pattern structures by adding or removing materials in order to restore a defective mask to good lithographic condition and, in many instances, it is an enabling step for yielding a defect-free mask. Beam-induced nano-structuring has been developed for such process with the use of photons, ions and electrons. However, it has become ever more challenging to repair advanced photomasks because of the limited extendability of these technologies to meet the critical defect specifications and tight edge placement. Specifically, the use of aggressive optical proximity correction structures, resolution enhancement techniques, such as phase-shifting, and entirely new types such as EUV reflective masks has placed a great need for stringent lateral and vertical dimensional control. A capable repair process removes the defect with sufficient placement precision while at the same time preserves the optical integrity of the repaired site. This essentially requires also a damage-free process. Mask shops have put ever increasing emphasis and effort in mask repair at the back end of the production line to fix every defect possible in order to restore an otherwise defective mask. This invited talk will present an overview of advanced mask repair and the lithographic requirements, followed by an assessment of four repair technologies by comparing their respective uniqueness and limitations. The discussion of underlying mechanisms for different repair processes will provide an insight to the fundamental capabilities and ways for further improvements. Detailed descriptions will be given for examples representing binary Cr-on-glass, phase-shifting and EUV masks including repair qualification. I will present our recent progress in electron beam mask repair development and discuss future directions in mask repair using nano-structuring technologies to support the aggressive lithography roadmap