In this talk, I will discuss various aspects of the gravitational path integral (GPI) approach to cosmology. First, I will revisit the Hartle-Hawking no-boundary proposal taking into account the norms of states computed using the GPI, and explain how this dramatically alters the predictions of the proposal. I will then propose an alternative prescription, which relates cosmological initial conditions to asymptotically AdS boundary conditions. Preliminary results show this approach predicts a long inflationary period ending in a metastable de Sitter universe (modulo some technical issues I will discuss). Finally, if time allows, I will comment on recent results that the Hilbert space of closed universes is one-dimensional, and discuss the role of an ingredient common to all proposed resolutions of this issue: ensemble averaging.