  The rather precise knowledge of the mass of the Higgs boson and of its
couplings has important consequences for the physical phenomena taking place at
the Fermi scale. We analyze some of these implications in the most motivated
frameworks for physics at that energies - supersymmetry, models of a composite
Higgs boson, and the Standard Model itself. At the same time, precision
experiments in flavour physics require a highly non-generic structure of
flavour and CP transitions. In any model of electroweak symmetry breaking with
a relatively low scale of new phenomena, as motivated by naturalness, some
mechanism has to be found in order to keep unwanted flavour effects under
control. We devote particular attention to the consequences of the approximate
U(2)^3 symmetry exhibited by the quarks of the Standard Model. The combined
analysis of the indirect constraints from flavour, Higgs and electroweak
physics will allow us to outline a picture of some most natural models of
physics near the Fermi scale. Although non trivially, a few models emerge that
look capable of accommodating a 125 GeV Higgs boson, consistently with all the
other constraints, with new particles in an interesting range for discovery at
the LHC, as well as associated flavour signals. This is particularly
interesting in view of the forthcoming improvements in the direct experimental
investigation of that energies. Finally, the measurement of the last parameter
of the Standard Model - the Higgs quartic coupling - has important consequences
even if no new physics is present close to the Fermi scale: its near-critical
value, which puts the electroweak vacuum in a metastable state close to a phase
transition, may have an interesting connection with Planck-scale physics. We
derive the bound for electroweak vacuum stability with full two-loop precision,
and explore some possible implication of near-criticality.
