  Gauge-Yukawa Unification (GYU) is a renormalization group invariant
functional relation among gauge and Yukawa couplings which holds beyond the
unification point in Grand Unified Theories (GUTs). We present here various
models where GYU is obtained by requiring the principles of finiteness and
reduction of couplings. We examine the consequences of these requirements for
the low energy parameters, especially for the top quark mass. The predictions
are such that they clearly distinguish already GYU from ordinary GUTs. It is
expected that it will be possible to discriminate among the various GYUs when
more accurate measurements of the top quark mass are available.
