  All-loop Finite Unified Theories (FUTs) are very interesting N=1
supersymmetric Grand Unified Theories (GUTs) which not only realise an old
field theoretic dream but also have a remarkable predictive power due to the
required reduction of couplings. The reduction of the dimensionless couplings
in N=1 GUTs is achieved by searching for renormalization group invariant (RGI)
relations among them holding beyond the unification scale. Finiteness results
from the fact that there exist RGI relations among dimensionless couplings that
guarantee the vanishing of all beta-functions in certain N=1 GUTs even to all
orders. Furthermore developments in the soft supersymmetry breaking sector of
N=1 GUTs and FUTs lead to exact RGI relations, i.e. reduction of couplings, in
this dimensionful sector of the theory too. Based on the above theoretical
framework phenomenologically consistent FUTS have been constructed. Here we
present FUT models based on the SU(5) and SU(3)^3 gauge groups and their
predictions. Of particular interest is the Higgs mass prediction of one of the
models which is expected to be tested at the LHC.
