We will explain how to apply the framework of noncommutative geometry in the setting of conformal geometry. We plan to describe three main results. The first result is a reformulation of the local index formula of Atiyah-Singer in conformal geometry, i.e., in the setting of the action of a group of conformal-diffeomorphism. The second result is the construction of new conformal invariants out of equivariant characteristic classes. The third result is a version in conformal geometry of the Vafa-Witten inequality for eigenvalues of Dirac operators. This is joint work with Hang Wang (University of Adelaide)