This is a review of the status and outstanding issues in attempts toconstruct chiral lattice gauge theories by decoupling the mirror fermions froma vectorlike theory. In the first half, we explain why studying nonperturbativechiral gauge dynamics may be of interest, enumerate the problems that a latticeformulation of chiral gauge theories must overcome, and briefly review ourcurrent knowledge. We then discuss the motivation and idea of mirror-fermiondecoupling and illustrate the desired features of the decoupling dynamics by asimple solvable toy model. The role of exact chiral symmetries and matching of't Hooft anomalies on the lattice is also explained. The second, moretechnical, half of the article is devoted to a discussion of the known andunknown features of mirror-decoupling dynamics formulated with Ginsparg-Wilsonfermions. We end by pointing out possible directions for future studies.
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