 In 2004, it was discovered that general relativity admits even more kinds of singularities than those known before, so-called ‘sudden singularities’ (Barrow 2004a, 2004b). The characterization of this kind of singularity has, so far, been confined to the context of cosmological models, including essentially all spacetimes whose matter content consists of homogeneous perfect fluids and a very wide class of spacetimes consisting of inhomogeneous fluids. The dynamics of those cosmological models is largely governed by the behavior of the cosmological expansion factor, a measure of the relative sizes of local regions of space (not spacetime) at different cosmological times. In an expanding spacetime, such as the one we believe ourselves to live in, the expansion factor continually increases, having “started from zero at the Big Bang”. If the universe's expansion stops, and the net gravitational effect on cosmological scales results in the universe's collapsing in on itself, this would be marked by a continual decrease in the expansion factor, eventuating in a Big Crunch singularity as the expansion factor asymptotically approached zero. The remaining dynamics of these cosmological models is encoded in the behavior of the Hubble parameter, a natural measure of the rate of change of the expansion factor. A sudden singularity, then, is defined by the divergence of a time derivative of the expansion factor or the Hubble parameter, though the factor or parameter itself remains finite. 