The phenomenological implications of the Standard Model (SM) are governed by
the accidental symmetry structure of the dimension-4 Lagrangian. In this
talk I discuss the next order in an expansion in the Higgs field and in
derivatives, that parametrize the largest effects of physics beyond the SM.
The remaining symmetries of this dimension-6 Lagrangian imply relations
between experimental observables that should be used to test the consistency
of deviations from the SM and to design precision New Physics searches.
