  Strong theoretical arguments suggest that the Higgs sector of the Standard
Model of the Electroweak interactions is an effective low-energy theory, with a
more fundamental theory that is expected to emerge at an energy scale of the
order of the TeV. One possibility is that the more fundamental theory be
strongly interacting and the Higgs sector be given by the low-energy dynamics
of the underlying theory. We review recent works aimed to determining
observable quantities by numerical simulations of strongly interacting theories
proposed in the literature for explaining the Electroweak symmetry breaking
mechanism. These investigations are based on Monte Carlo simulations of the
theory formulated on a spacetime lattice. We focus on the so-called Minimal
Walking Technicolour scenario, a SU(2) gauge theory with two flavours of
fermions in the adjoint representation. The emerging picture is that this
theory has an infrared fixed point that dominates the large distance physics.
We shall discuss the first numerical determinations of quantities of
phenomenological interest for this theory and analyse future directions of
quantitative studies of strongly interacting beyond the Standard Model theories
with Lattice techniques. In particular, we report on a finite size scaling
determination of the chiral condensate anomalous dimension $\gamma$, for which
we find $0.05 \le \gamma \le 0.25$.
