!!!  in person only  !!!

I will discuss the gravitational path integral in the context of the supersymmetric index. In the last five years or so, supersymmetric and non-extremal ("finite-temperature") saddle-points of this gravitational index have been discovered. These saddles encode the free energy of supersymmetric black holes. I will review these developments, focussing on four-dimensional black holes in asymptotically flat space. I will then show how a class of 5d solutions can be constructed using the 4d-5d lift. On one hand, these solutions compute the index of black holes and black strings in asymptotically flat 5d space, even in the absence of an AdS near-horizon region. On the other hand, a novel decoupling limit of the black string solution gives a finite-temperature BTZ black hole that computes the index in AdS3/CFT2.