Going beyond the Standard Model Higgs at the Large Hadron Collider

Up to date and within the available accuracy, the results of the CERN LHC experiment agree with the predictions of the Standard
Model. This leaves unanswered the crucial question of what physics lies behind the breaking of the electroweak symmetry at the Fermi scale. I will discuss theoretical approaches to this problem, focussing in particular on the idea that the observed Higgs particle may be approximately described as a Goldstone boson coming from a new physics sector. This includes long-standing models partly inspired by QCD, as weel as more recently-proposed 'Twin Higgs' theories, where the particles of the new sector do not interact directly with the Standard Model, thus potentially explaining the absence of any signals at the LHC. I will emphasize the strategies to probe these possibilities at colliders.