Chiral Symmetry Outside Perturbation Theory

Within the overlap framework, I derive the main formulae one finds today in papers touting a ``new approach'' to the regularization of chiral gauge theories. My main objective is to clear up an unhealthy confusion about how many successful approaches to regulate chiral fermions on the lattice there really are: At the moment, there is only one, the overlap, and finding a genuinely different approach is an important and completely open problem.