Quantum gravity: are we there yet?

The turn of the millennium was a time of optimism about an approach to non-commutative geometry inspired by rich mathematical objects called 'quantum groups' and its applications to quantum spacetime. The idea was to model quantum gravity effects as non-commutativity of spacetime coordinates and arguably solve quantum gravity itself. This required, however, a 20-year development of a suitable formalism of quantum Riemannian geometry (QRG) to handle such coordinates, which I outline here. I then provide new results for state-of-the-art fuzzy sphere and [Formula: see text]-gon 'baby quantum gravity' models in this approach and some possible features of quantum gravity that these models suggest. Also discussed are the critical conceptual and mathematical elements that are still missing to more fully achieve this goal.This article is part of the theme issue 'Science into the next millennium: 25 years on'.