This article reviews the construction and properties of three-dimensional 'quantum' black holes, which arise from holographic braneworlds and are exact solutions to a higher-derivative theory of gravity coupled to a large-$c$ quantum field theory with an ultraviolet cutoff. These quantum-corrected black holes are much larger than the Planck length. The authors describe the geometry and horizon thermodynamics of various asymptotically (anti-) de Sitter and flat quantum black holes, and provide a summary of higher-dimensional extensions. They also survey multiple applications of quantum black holes and braneworld holography, including the study of semi-classical horizon thermodynamics, holographic entanglement entropy, and complexity, as well as the prospect of probing black hole singularities. The primary purpose of the review is to explore the state of the art in holographic quantum black holes, with a focus on analytic black holes that localize on an AdS$_4$ braneworld, and to advertise the applications of these constructions in testing ideas in semi-classical/quantum gravity.This article reviews the construction and properties of three-dimensional 'quantum' black holes, which arise from holographic braneworlds and are exact solutions to a higher-derivative theory of gravity coupled to a large-$c$ quantum field theory with an ultraviolet cutoff. These quantum-corrected black holes are much larger than the Planck length. The authors describe the geometry and horizon thermodynamics of various asymptotically (anti-) de Sitter and flat quantum black holes, and provide a summary of higher-dimensional extensions. They also survey multiple applications of quantum black holes and braneworld holography, including the study of semi-classical horizon thermodynamics, holographic entanglement entropy, and complexity, as well as the prospect of probing black hole singularities. The primary purpose of the review is to explore the state of the art in holographic quantum black holes, with a focus on analytic black holes that localize on an AdS$_4$ braneworld, and to advertise the applications of these constructions in testing ideas in semi-classical/quantum gravity.