Abstract: I will discuss one of the simplest theories of quantum gravity, three-dimensional Einstein gravity with negative cosmological constant. Although it has no gravitational waves, the theory admits black hole solutions and is expected to be holographically dual to a two-dimensional conformal field theory, making it a natural laboratory for basic questions in quantum gravity. I will describe a reformulation of AdS_3 quantum gravity in terms of a novel topological quantum field theory that we refer to as “Virasoro TQFT.” This framework allows the gravitational path integral to be computed exactly on a fixed spacetime topology. It also sharpens the idea that the gravitational path integral captures coarse-grained statistical properties of the holographic dual. I will then survey several recent applications of this technology, from the sum over topologies to de Sitter space.