The central dogma states that a black hole behaves as an ordinary quantum system viewed from the outside. This has been realized in holography via the Ryu-Takayanagi formula, which associates a bulk surface to a measure of boundary quantum entanglement. As an incarnation of holographic entanglement entropy, the bulk extremal surface leads to the paradigm of entanglement wedge reconstruction. We discuss two applications of this paradigm that connect with quantum chaos and black holes. First, by considering the entanglement wedge associated with a boundary subregion, one can define a notion of operator size in the boundary and determine the butterfly velocity that characterizes the growth of local perturbations from certain extremal surfaces. However, the study of quantum chaos presents a novel bound to holographic theories through a distinct Lorentzian calculation of the butterfly velocity, determined from a localized shockwave on the horizon of a dual black hole. We demonstrate a general agreement between the two pictures in higher-curvature gravity, revealing deep connections between quantum chaos and holography. Second, the entanglement wedge of Hawking radiation leads to quantum extremal islands, offering a resolution to the black hole information loss problem. We explore the method within a less understood non-minimal dilaton gravity model that traces back to an old puzzle about Hawking radiation that leads to black hole "anti-evaporation." By identifying the choice of state with Weyl-invariant terms of the one-loop effective action, we construct quantum stress tensors in both eternal and evaporating black holes that resolve the puzzle. Along the way, we discuss potential generalizations and applications of the models.