The conformal method was introduced by Roger Penrose in the early 1960’s as a means of describing infinity of a spacetime as a finite boundary for a spacetime whose metric is the original one rescaled by a positive function that vanishes at the boundary, but not its differential. Such a construction is called a conformal compactification. He applied the method to Minkowski, Schwarzschild, Kerr spacetimes. For the simplest case, Minkowski spacetime, the compactification actually gives rise to a compact spacetime, which is exceptional. There is another natural way of compactifying Minkowski spacetime that is weaker because we do not construct the whole boundary, however, it has the advantage of being stable in the sense that a similar compactification exists for Schwarzschild and Kerr metric. We present the two constructions.