We argue for enlarging the traditional view of quantum gravity, based on ‘quantizing GR’, to include explicitly the nonspatiotemporal nature of the fundamental building blocks suggested by several modern quantum gravity approaches (and some semiclassical arguments) and to focus more on the issue of the emergence of continuum spacetime and geometry from their collective dynamics. We also discuss some recent developments in quantum gravity research, aiming at realizing these ideas, in the context of group field theory, random tensor models, simplicial quantum gravity, loop quantum gravity, and spin foam models.