Conformal compactifications were introduced by Penrose to study the asymptotic behavior of vacuum spacetimes in general relativity and have since been extensively studied by H. Friedrich, Christodoulou, Klainerman and many others. This idea and related renormalization procedures have also arisen recently in the AdS/CFT correspondence relating gravity in the bulk with gauge theory on the boundary in physics. We will introduce the well-known Fefferman Graham obstruction tensor and show how it can be used, quite easily, to study conformal compactifications of the vacuum Einstein equations, for all values of the cosmological constant. This gives new and simple proofs of results of H. Friedrich in 3+1 dimensions, and generalizes these results to all even dimensions.