Abstract: I will discuss two topics in quantum gravity, both involving the gravitational path integral. In the first part I will introduce the “no-boundary wave function”, a path integral over geometries on compact four-manifolds which solves the Wheeler-DeWitt equation. I will then outline how this object can be computed, and comment on its interpretation, in the scenario of minimally coupled scalar field matter subject to a potential energy function of the slow-roll type. In the second part I will comment on a proposal which identifies bulk gravitational path integrals with ensemble averages of boundary partition functions. This talk is based on 2009.06282 and work in progress.