Gravitational waves offer an unprecedented window into the fundamental physics of black holes, which allows us to probe complex nonlinear and transient behaviors. In this talk, I will present our recent progress in characterizing these phenomena, focusing on the nonlinear (resonant) excitation of quasinormal modes, (non)linear tails, and the emergence of turbulent-like energy cascades. I will also discuss transient features, such as the prompt response, and their implications for our understanding of strong-field gravity.