N = 1 supersymmetric GUTs that can be made finite to all orders are called Finite Unified Theories (FUTs). These theories are based on the principle of the reduction of couplings, which consists of searching for renormalization group invariant (RGI) expressions among parameters holding to all orders. FUTs predicted the top quark mass one and half years before its experimental discovery, while four and a half years before the Higgs boson discovery, a particular FUT predicted the light Higgs boson mass in the range ~121–126 GeV, in striking agreement with the LHC discovery. We review the basic properties of supersymmetric finite theories resulting from reduction of couplings in both their dimensionless and dimensionful sectors. Then, we analyse the SU(5)-based FUT, which is favoured from a phenomenological point of view. This particular FUT leads to a version of the MSSM that is constrained by the finiteness conditions at the unification scale and predicts a relatively heavy spectrum with coloured supersymmetric particles above 2.7 TeV, consistent with the non-observation of those particles at the LHC. The electroweak supersymmetric spectrum starts below 1 TeV, while parts of the allowed spectrum could be accessible at CLIC. The FCC-hh is expected to be able to fully test the predicted spectrum.