The study of black holes resonant excitation and their subsequent relaxation ("Black Hole Spectroscopy") is a fundamental tool to observationally investigate gravity in its most dynamical and violent regime. The unprecedented loudness of the gravitational wave signal GW250114 - enabled by the exquisite measurement precision of ground-based interferometers - recently allowed us to exploit spectroscopic techniques to achieve the first accurate verification of two long-standing predictions of general relativity: Hawking's Area Law and the Kerr nature of the source. I will discuss these fascinating results, the data-analysis and modelling challenges behind them, and the ultimate limitations of these investigations.

Indeed, despite the striking simplicity of black holes, and decades of developments in classical perturbation theory, many dynamical and nonlinear properties of black holes remain unknown. Such ignorance prevents even more exciting explorations of the enigmatic phase in which two black holes fuse together, the "merger" regime. In the last part of the seminar, I will summarise recent breakthroughs in this direction, and their potential to advance our understanding of gravity, searches for new physics, and to harvest the full potential of next-generation detectors.