  Chiral fermions resisted being put on the lattice for twenty years. This
raised the suspicion that asymptotically free chiral gauge theories were not
renormalizable outside perturbation theory and therefore could not be
mathematically extended to infinite energies. During the last several years the
situation has reversed itself. Today we believe that all the essential
ingredients for a full lattice definition of non-anomalous chiral gauge
theories are in place within the overlap construction. This construction is
based on earlier work by Callan and Harvey, by Kaplan and by Frolov and
Slavnov. It can be reinterpreted as coming from the Ginsparg-Wilson relation,
but, at the moment, it is a unique construction and therefore might also be the
way by which Nature itself regularizes chiral fermions. This is yet another
instance in which lattice field theory makes a potentially important
contribution to fundamental particle physics.
