In this thesis, we present our work on computing signatures of quantum chaos in gravity. More specifically, we show how higher topologies in the gravitational path integral-called Euclidean wormholes- encode statistical properties of the data of strongly coupled Conformal Field Theories (CFTs) thereby establishing how quantum gravity realizes a version of the Eigenstate Thermalization Hypothesis (ETH) based on the randomness of CFT data. First, we propose a novel correspondence between wormhole solutions to Einstein's equations in semiclassical 3D gravity and averages of corresponding observables in 2D CFT and support out proposal using several examples. We then discuss the construction of wormholes in higher dimensions sourced by spherically symmetric thin shells of dust particles and interpret them in individual CFTs in terms of coarse-graining CFT data. Developing this idea further, we establish a correspondence between the statistics of black holes formed from such dust shells in 3D gravity and the dynamics of a non-conformal line defect in 2D CFT. We also construct wormholes using domain wall solutions in AdS/CFT and show how these wormholes capture covariances between observables in different CFTs thereby providing a precision test for the realization of ETH in gravity. As an interesting application, by employing information-theoretic ideas, we construct a quantitative random tensor network model for black holes using CFT data, which exhibits essential features of the black hole interior.