  The general theory of the reduction in the number of coupling parameters is
discussed. The method involves renormalization group invariant relations
between couplings. It is more general than the imposition of symmetries. There
are reduced theories with no known symmetry. The reduction scheme is finding
many applications. Discussed in some detail are the construction of gauge
theories with ``minimal'' coupling for Yang-Mills and matter fields, and the
Gauge-Yukawa Unification within N=1 supersymmetric GUT's.
