A particle with the quantum numbers and properties of the Higgs was discovered two years ago. Is this Higgs truly elementary? How much room is left for compositeness? Is the Standard Model all that there is? I shall attempt to give a partial answer to these questions by considering extended electroweak symmetry breaking sectors, parametrized in terms of an effective theory, and imposing on it the requirements of unitarity and causality. Unitarization of the amplitudes will imply a number of new resonances in this type of models and their presence or absence will severely constrain extensions of the standard model. Current experimental results still allow for such resonances and the Higgs might be not elementary after all in spite of its Standard Model appeareance.