I will discuss how the Standard Model of particle physics can emerge consistently (in the form of an effective field theory) as the long-distance approximation of radically different theories, based possibly on strongly coupled dynamics. These broad scenarios of vector/fermion/scalar compositeness, constitute the primary target for precision tests of the Standard Model, performed at the LHC. I discuss the implications of interesting BSM-SM non-interference rules, that can be simply derived using scattering amplitudes techniques, and provide an additional challenge for a precision program.