The talk will review well known unsolved questions in quantum gravity, such as non-renormalizability, UV incompleteness and absence of non-perturbative local observables. I will next show that Anti de Sitter (AdS) space in three space-time dimensions is a useful toy model of quantum gravity since it retains some of the most puzzling features in a vastly simplified context. Among the former are the presence of black holes and infinite-dimensional asymptotic symmetries as well as the absence of local observables; among the latter, the absence of local dynamics. I will also explain in what sense pure 3D AdS gravity may admit a simpler "square root" theory and how high-spin excitations, while non-propagating inside AdS3, are described by non-trivial, non-free field theories. Such theories model certain aspects of more complex high-spin theories in dimension 4 or higher.
