Since Hawking proved his singularity theorem, it is clear that singularities of big bang type typically occur in cosmological solutions to Einstein’s equations. For many matter models, solutions are expected to exhibit chaotic dynamics governed by the so-called BKL map, but for some matter models, the dynamics are expected to be quiescent. The purpose of the talk is to discuss quiescent singularities, with an emphasis on a geometric notion of initial data on the singularity.