  In this review we summarize the ongoing effort to study extra-dimensional
gauge theories with lattice simulations. In these models the Higgs field is
identified with extra-dimensional components of the gauge field. The Higgs
potential is generated by quantum corrections and is protected from
divergencies by the higher dimensional gauge symmetry. Dimensional reduction to
four dimensions can occur through compactification or localization. Gauge-Higgs
unification models are often studied using perturbation theory. Numerical
lattice simulations are used to go beyond these perturbative expectations and
to include non-perturbative effects. We describe the known perturbative
predictions and their fate in the strongly-coupled regime for various
extra-dimensional models.
