Among submanifolds,hypersurfaces are particularly important for geometric analysis as they arise as boundaries of domains and manifolds.We discuss the treatment of conformal hypersurfaces,and in particular the construction of canonical invariant di erential operators along a hypersurface in a conformal manifold.The operators constructed have applications in the construction of higher order conformally invariant Dirichlet-to-Neumann operators(that may be interpreted as conformally invariant fraction powers of the Laplacian).Associated to the operators are interesting curvature quantities that in a conformal sense generalise the mean curvature and the T-curvature of Chang-Qing.The operators also shed light on conjectures of Juhl.This is joint work with Larry Peterson.