Shape dynamics is dynamically equivalent to the canonical formulation of general relativity, known as the ADM formalism. Shape dynamics is not formulated as an implementation of spacetime diffeomorphism invariance, but as an implementation of spatial relationalism based on spatial diffeomorphisms and spatial Weyl symmetry. An important consequence of shape dynamics is the absence of a problem of time in canonical quantum gravity. The replacement of the spacetime picture with a picture of evolving spatial conformal geometry opens the door for a number of new approaches to quantum gravity.