The Hawking-Penrose theorems tell us that solutions of Einstein’s equations are generally singular, in the sense of the incompleteness of causal geodesics (the paths of physical observers). These singularities might be marked by the blowup of curvature and therefore crushing tidal forces, or by the breakdown of physical determinism. Penrose has conjectured (in his "Strong Cosmic Censorship Conjecture") that it is generically unbounded curvature that causes singularities, rather than causal breakdown. The verification that "AVTD behavior" (marked by the domination of time derivatives over space derivatives) is generically present in a family of solutions has proven to be a useful tool for studying model versions of Strong Cosmic Censorship in that family. I discuss some of the history of Strong Cosmic Censorship, and then discuss what is known about AVTD behavior and Strong Cosmic Censorship in families of solutions defined by
varying degrees of isometry, and discuss recent results which we believe will extend this knowledge and provide new support for Strong Cosmic Censorship. I also comment on some of the recent work on "Weak Null Singularities", and how this relates to Strong Cosmic Censorship.