2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/101126We discuss a number of topics in the area of conformally compact Einstein metrics, mostly centered around the global existence question of finding such metrics with an arbitrarily prescribed conformal infinity. The paper is partly a survey of this area but also presents new results and a number of open problems.24pp, to appear in Proc. CRM, MontrealDifferential Geometrytext