We begine with a discussion of the key problems, viz. the construction of natural
invariants and invariant operators for conformally embedded
hypersurfaces. These have applications in Scattering, String theory
(especially surrounding the AdS/CFT programme, PDE boundary problems,
and representation theory.
Then we discuss: Tractor calculus. Hypersurface tractor
theory. The proliferation of conformally invariant boundary
operators, and connectionsof these to $Q$ and $T$ curvatures.