2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/34188This talk reports on the status of an approach to the numerical study of isolated systems with the conformal field equations. We first describe the algorithms used in a code which has been developed at AEI in the last years, and discuss a milestone result obtained by Huebner. Then we present more recent results as examples to sketch the problems we face in the conformal approach to numerical relativity and outline a possible roadmap toward making this approach a practical tool.20 pages, to appear in the proceedings of the conference ``The Conformal Structure of Spacetimes: Geometry, Analysis, Numerics'', ed. by J. Frauendiener and H. Friedrich, to be published by Springer Verlag, Lecture Notes in Physics seriesGeneral Relativity and Quantum Cosmologytext