Numerical evolutions show that, in spherical symmetry, as we move through the solution space of GR to the threshold of black hole formation, the resulting spacetimes tend to display a surprising degree of simplicity. A heuristic description of this behavior, called critical collapse, has been built around this empirical fact. Less is known when symmetry is dropped. In this presentation I will review the current status of the topic, focusing in particular on the struggle to understand the situation in axisymmetry.
