  Lattice formulations of QCD with Wilson fermions and a chirally twisted quark
mass matrix provide an attractive framework for non-perturbative numerical
studies. Owing to reparameterization invariance, the limiting continuum theory
is just QCD. No spurious quark zero modes, which are responsible for the
problem with exceptional configurations, can occur at finite values of the
quark mass. Moreover, the details of the lattice formulation can be adjusted so
as to simplify the renormalization and the O($a$) improvement of several
quantities of phenomenological relevance. The first exploratory studies in the
quenched approximation yield very encouraging results.
