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We discuss the role of wormholes and branes in reconciling geometry with quantum mechanics, based on recent developments in JT gravity, an analytically solvable model of quantum gravity in two dimensions. First, we will see how wormholes enable geometry to accurate capture averaged correlators of chaotic quantum systems. Because these are averaged properties, naively wormholes in gravitational theories imply some ensemble interpretation of those theories. However, we will see that the geometrical description of individual quantum systems involves not just wormholes, but also some background branes. These branes encode the microstructure of some given quantum system in bulk geometry and collapse the ensemble.