  An extension of the ambient metric construction of Fefferman-Graham to
infinite order in even dimensions is described. The main ingredients are the
introduction of "inhomogeneous ambient metrics" with asymptotic expansions
involving the logarithm of a defining function homogeneous of degree 2, and an
invariant procedure for taking the smooth part of such an inhomogeneous ambient
metric. The metrics which result depend on the choice of an "ambiguity tensor"
as well as a conformal class. An application to the description of scalar
conformal invariants in even dimensions is outlined.
