2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/35975The last seven years has produced a growing body of evidence which concludes that the Cauchy horizon in black hole-de Sitter spacetimes is classically stable when the surface gravity at the cosmological event horizon is greater than that at the Cauchy horizon. That stability persists for a finite, but non-zero, region of the black hole's parameter space, $(M,Q,J,Λ)$, suggests that black holes immersed in de Sitter space are counter-examples to the strong cosmic censorship hypothesis. In this review we chronicle that body of evidence and describe the first steps of a program of numerical work aimed at better understanding the interior of black hole-de Sitter spacetimes. The review ends with a speculative account of the role that future work will take.35 pages (including 15 eps figures), RevTex. Uses header.sty (included). To be published in the proceedings of the workshop on ``The Internal Structure of Black Holes and Spacetime Singularities", held at the Technion -- Israel Institute of Technology, Haifa, Israel. June 29 - July 3, 1997General Relativity and Quantum Cosmologytext