The LHC might (have) discover(ed) a Higgs boson but it will have a harder time telling whether this boson is an elementary scalar field. I shall describe models with a Higgs emerging as a composite bound state from a strongly interacting sector and I shall report on the study of various processes both at the LHC and at a linear collider which can probe the strong sector and can help distinguishing strong from weak models of electroweak symmetry breaking.