  The 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, $(M,Q,J,\Lambda)$,
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.
