  Composite Higgs Models explore the possibility that the Higgs boson is an
excitation of a new strongly interacting sector giving rise to electro-weak
symmetry breaking. After describing how this new sector can be embedded into
the Standard Model of elementary particle physics meeting experimental
constraints, I will review efforts by the community to explore the physics of
the new strong interaction using methods of lattice field theory. Challenges in
understanding the numerical results are discussed and an outlook is given on
possible future directions allowing to confirm or reject the composite Higgs
hypothesis.
