  In this thesis we study some theoretical and phenomenological aspects of
classical conformal symmetry in specific extensions of the SM. We consider both
supersymmetric and non supersymmetric cases. We discuss the perturbative
structure of the superconformal anomaly effective action. We show that the
manifestation of the anomaly is in the presence of massless intermediate states
in correlators involving the Ferrara-Zumino supercurrent with two vector
supercurrents. This universal feature is typical both of chiral and conformal
anomalies. These results are used in a study of a possible extension of the SM
with a dilaton, deriving some bounds on a possible conformal scale. Then we
turn to investigate a specific superconformal theory, the TNMSSM, which extends
the MSSM with one extra triplet and a scalar singlet superfield. The
manifestation of the classical conformal symmetry in this model is in the
existence of a very light pseudoscalar in the physical spectrum. We study the
main proprieties of this state and its potential discovery at the LHC. In the
last part of this work we discuss an application of the graviton-photon-photon
vertex to gravitational lensing for a Schwarzschild background. In particular,
we introduce the notion of a semiclassical lens equation for the deflection of
a photon nearing the horizon of a black hole.
