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.