  We discuss the relation between the $c$--theorem and the the way various
symmetries are realized in quantum field theory. We review our recent proof of
the $c$--theorem in four dimensions. Based on this proof and further evidence,
we conjecture that the realization of chiral symmetry be irreversible, flowing
from the Wigner-Weyl realization at short distance to the Nambu--Goldstone
realization at long distance. We argue that three apparently independent
constraints based on the renormalization group, namely anomaly matching, the
c-theorem and the conjectured symmetry realization theorem, are particular
manifestations of a single underlying principle.
