  Hypersurfaces embedded in conformal manifolds appear frequently as boundary
data in boundary-value problems in cosmology and string theory. Viewed as the
non-null conformal infinity of a spacetime, we consider hypersurfaces embedded
in a Riemannian (or Lorentzian) conformal manifold. We construct a finite and
minimal family of hypersurface tensors -- the curvatures intrinsic to the
hypersurface and the so-called ``conformal fundamental forms'' -- that can be
used to construct natural conformal invariants of the hypersurface embedding up
to a fixed order in hypersurface-orthogonal derivatives of the bulk metric. We
thus show that these conformal fundamental forms capture the extrinsic
embedding data of a conformal infinity in a spacetime.
