  Finite Unified Theories (FUTs) are N = 1 supersymmetric Grand Unified
Theories (GUTs) which can be made finite to all-loop orders, based on the
principle of reduction of couplings, and therefore are provided with a large
predictive power. Confronting the predictions of SU(5) FUTs with the top and
bottom quark masses and other low-energy experimental constraints a light
Higgs-boson mass in the range M_h \sim 121-126 GeV was predicted, in striking
agreement with the recent discovery of a Higgs-like state around \sim 125.5 GeV
at ATLAS and CMS. Furthermore the favoured model, a finiteness constrained
version of the MSSM, naturally predicts a relatively heavy spectrum with
coloured supersymmetric particles above \sim 1.5 TeV, consistent with the
non-observation of those particles at the LHC. Restricting further the best
FUT's parameter space according to the discovery of a Higgs-like state and
B-physics observables we find predictions for the rest of the Higgs masses and
the supersymmetric particle spectrum.
