 Whereas (perturbative) string theory and other so-called ‘covariant’ approaches view the curved spacetime of general relativity as an effective modification of a flat (or other fixed) background geometry by a massless spin-two field, the canonical quantum gravity program treats the full spacetime metric itself as a kind of field, and attempts to quantize it directly without splitting it apart into a flat part and a perturbation. However, spacetime itself is split apart into a stack of three dimensional slices (a foliation) on which is defined a spatial geometry. Technically, work in this camp proceeds by writing down general relativity in so-called ‘canonical’ or ‘Hamiltonian’ form, since there is a more-or-less clearcut way to quantize theories once they are put in this form (Kuchar, 1993; Belot &amp; Earman, 2001). In a canonical description, one chooses a particular set of configuration variables xi and canonically conjugate momentum variables pi which describe the state of a system at some time, and can be encoded in a phase space. Then, one obtains the time-evolution of these variables from the Hamiltonian H(xi,pi), which provides the physically possible motions in the phase space a a family of curves. Quantization proceeds by treating the configuration and momentum variables as operators on a quantum state space (a Hilbert space) obeying certain commutation relations analogous to the classical Poisson-bracket relations, which effectively encode the quantum fuzziness associated with Heisenberg’s uncertainty principle. The Hamiltonian operator, acting on quantum states, would then generate the dynamical evolution.