Extracting the Universe from the Wave Function

Quantum mechanics is a theory of wave functions in Hilbert space. Many features that we generally take for granted when we use quantum mechanics -- classical spacetime, locality, the system/environment split, collapse/branching, preferred observables, the Born rule for probabilities -- should in principle be derivable from the basic ingredients of the quantum state and the Hamiltonian. I will discuss recent progress on these problems, including consequences for emergent spacetime and quantum gravity.