  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 ~ 121-126 GeV was predicted, in striking
agreement with the recent discovery of a Higgs-like state around ~ 125.7 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 ~ 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
s-spectrum.
