  The turn of the millennium was a time of optimism about an approach to
noncommutative geometry inspired by rich mathematical objects called `quantum
groups' and its applications to quantum spacetime. This would model quantum
gravity effects as noncommutativity of spacetime coordinates and was arguably
going to solve quantum gravity itself. It took a further 20 years from that
point to develop a particularly suitable formalism of `quantum Riemannian
geometry', but this was largely done and has begun to be used to construct baby
quantum gravity models. In this article, we obtain new results for state of the
art fuzzy sphere and n-gon models in this approach. We also review what are
some elements of quantum gravity that we can already see and what are the
critical conceptual and mathematical elements that are still missing to more
fully achieve this goal.
