 Whether or not spacetime is discrete, the quantization of spacetime entails that our ordinary notion of the physical world, that of matter distributed in space and time, is at best an approximation. This in turn implies that ordinary quantum theory, in which one calculates probabilities for events to occur in a given world, is inadequate as a fundamental theory. As suggested in the  Introduction,  this may present us with a vicious circle. At the very least, one must almost certainly generalize the framework of quantum theory. This is an important driving force behind much of the effort in quantum cosmology to provide a well-defined version of the  many-worlds  or  relative-state  interpretations. Much work in this area has adopted the so-called ‘decoherent histories’ or ‘consistent histories’ formalism, whereby quantum theories are understood to make probabilistic predictions about entire (coarse-grained) ‘histories’. Almost all of this work to date construes histories to be histories of spatiotemporal events, and thus presupposes a background spacetime; however, the incorporation of a dynamical, quantized spacetime clearly drives much of the cosmology-inspired work in this area.