  After the discovery of the Higgs boson, the primary objective of the Large
Hadron Collider (LHC) experiments is to identify new physics beyond the
Standard Model (SM). One of the most intriguing possibilities would be the
discovery of non-perturbative phenomena in electroweak physics. In fact both
ATLAS and CMS are providing crucial precision tests of the Higgs sector. Most
strikingly, there is no conclusive evidence yet on whether the Higgs boson is
elementary or composite. Lattice simulations can play a key role in advancing
our theoretical understanding of strongly coupled gauge theories relevant for
extensions of the SM and the LHC program. In this talk I will review the state
of beyond the SM (BSM) lattice studies aimed to chart the phase diagram and to
uncover the properties of strongly coupled gauge theories.
