About fifty years ago, Gibbons and Hawking argued that the Euclidean gravitational path integral with suitable boundary conditions can be interpreted as a grand-canonical partition function. Classical gravitational solutions, including black holes, arise as saddles of this path integral, and from the saddle-point action one can extract the black hole entropy. In the talk, I will discuss some recent developments of these ideas. Working in five dimensions, we will see how imposing supersymmetric boundary conditions converts the partition function into an index. Then we will construct a class of saddles of this index which interpolates between supersymmetric black holes and horizonless microstate geometries. I will discuss how the saddle point action can be computed via equivariant localization. Finally, I will comment on the relevance of these findings for black hole microstate counting and holography.