  We review some recent work on nonperturbative properties of fermions and
connections with chiral gauge theories. In particular, we consider one of the
ultimate goals of this program: the understanding of the actual fermion mass
spectrum. It is pointed out that if quarks and leptons are composite, their
masses may be set by the physics of the preons and their interactions in such a
manner as to differ considerably from the Yukawa form $m_f \propto v$ (where
$v$ is the electroweak symmetry breaking scale) or analogous forms involving
$v$. Some ideas of how this might work are given, and some implications are
discussed.
