Explore the intricacies of Liouville and JT Quantum Gravity in this 55-minute conference talk by Thomas Mertens from Ghent University, presented at the Online Workshop on Qubits and Black Holes. Delve into holography and matrix models, examining fixed-length boundaries, disk partition functions, and multi-boundary amplitudes. Investigate the JT limit, density of states, and Euclidean wormholes. Uncover the group theory interpretation of JT gravity and the quantum group interpretation of Liouville supergravity. Analyze the boundary two-point function and explore Liouville gravity as a dilaton gravity. Gain insights into black hole solutions and the first law, providing evidence for the quantum group interpretation of Liouville gravity.