Gauge-Yukawa Unification (GYU) is a renormalization group invariant fu
nctional relation among gauge and Yukawa couplings which holds beyond
the unification point in Grand Unified Theories (GUTs). We present her
e 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 t
op quark mass. The predictions are such that they clearly distinguish
already GYU from ordinary GUTs. It is expected that it will be possibl
e to discriminate among the various GYUs when more accurate measuremen
ts of the top quark mass are available.