Einstein field equations are not conformally invariant. Despite this fact, conformal geometry plays an important role in description of asymptotics of the solutions via so-called Penrose conformal compactification. Moreover, in many cases such conformal compactification of solution is smooth. It turns out that these facts are linked to a fundamental object in conformal geometry, Fefferman- Graham obstruction tensor. I will describe this connection in my talk, together with some interesting implications. The talk will last approximately 2x45 min with a break.