New Results in Theories with Reduced Couplings

The renormalization group invariant, to all orders in perturbation theory, relations among parameters consist the basis of the reduction of couplings concept. N=1 supersymmetric Grand Unified Theories can use the above concept, and even be finite at all loops. We review this idea as well as the resulting theories. We construct: (i) an $N=1$ $SU(5)$ minimal version, (ii) an all-loop finite $N=1$ $SU(5)$, (iii) a two-loop finite $N=1$ $SU(3)^3$ and finally (vi) a Minimal Supersymmetric Standard Model reduced version. The SUSY particle spectra predicted by these models are consistent with the LHC non-observation results.