  We study the dynamics of chiral SU(N) gauge theories. These contain Weyl
fermions in the symmetric or anti-symmetric representation of the gauge group,
together with further fermions in the fundamental and anti-fundamental. We
revisit an old proposal of Bars and Yankielowicz who match the 't Hooft
anomalies of this theory to free fermions. We show that there are novel and, in
some cases, quite powerful constraints on the dynamics in the large N limit.
  In addition, we study these SU(N) theories with an extra Weyl fermion
transforming in the adjoint representation. Here we show that all 21 't Hooft
anomalies for global symmetries are matched with those of a Spin(8) gauge
theory. This suggests a non-supersymmetric extension of the duality of Pouliot
and Strassler. Finally, we also discuss some non-supersymmetric dualities with
vector-like matter content for SO(N) and Sp(N) gauge theories and the
constraints imposed by Weingarten inequalities.
