  The idea of reduction of couplings consists in searching for renormalization
group invariant relations between parameters of a renormalizable theory that
hold to all orders of perturbation theory. Based on the principle of the
reduction of couplings, one can construct Finite Unified Theories (FUTs) which
are $N=1$ supersymmetric Grand Unified Theories that can be made all-order
finite. The prediction of the top quark mass well in advance of its
experimental discovery and the prediction of the light Higgs boson mass in the
range $\sim 121-126$ GeV much earlier than its experimental discovery are among
the celebrated successes of such models. Here, after a brief review of the
reduction of couplings method and the properties of the resulting finiteness in
supersymmetric theories, we analyse four phenomenologically favoured models: a
minimal version of the $N=1$ $SU(5)$, a finite $N=1$ $SU(5)$, a $N=1$ finite
$SU(3)\otimes SU(3)\otimes SU(3)$ model and a reduced version of the Minimal
Supersymmetric Standard Model (MSSM). A relevant update in the phenomenological
evaluation has been the improved light Higgs-boson mass prediction as provided
by the latest version of $\texttt{FeynHiggs}$. All four models predict
relatively heavy supersymmetric spectra that start just below or above the TeV
scale, consistent with the non-observation LHC results. Depending on the model,
the lighter regions of the spectra could be accessible at CLIC, while the
FCC-hh will be able to test large parts of predicted spectrum of each model.
The lightest supersymmetric particle (LSP), which is a neutralino, is
considered as a cold dark matter candidate and put to test using the latest
$\texttt{MicrOMEGAs}$ code.
