We discuss general aspects of CFT’s in d> 2 dimensions and the solution of the conformal constraints (conformal Ward identities) for 3-point scalar and tensor correlators in momentum space. This allows us to investigate the role of the conformal anomaly in great generality. The matching of a general CFT to free-field theory realizations allows us to simplify drastically the solution of the conformal Ward identities and the structure of such tensor correlators. We then turn to 4-point functions, showing the existence of solutions of such identities in the presence of a conformal/dual conformal symmetry. Some phenomenological implications of CFT in physics beyond the Standard Model will also be briefly outlined.
