This workshop brings together mathematicians and physicists working on the dynamics of black holes. The event will explore recent breakthroughs in the stability of black holes, as well as the many remaining open questions, particularly in the near-extremal or extremal case. Topics will include longtime dynamics of black hole perturbations, including scattering problems, nonlinear studies, quasinormal modes, and unstable behaviors in both four and higher dimensions. As this is a very interdisciplinary area of research, we plan on having speakers spanning the continuum between physics and mathematics of General Relativity.