The direct detection of gravitational waves from merging binary systems marked a major breakthrough in physics. As we move toward the era of precision physics with gravitational waves with next-generation space and ground-based interferometers, one key observable will be the tidal deformability of the coalescing objects. The tidal deformability is characterized in terms of complex coefficients, whose real (i.e., conservative) parts are often referred to as Love numbers. The Love numbers are important because they offer insights into the gravitational behavior and the body’s internal structure. In the case of black holes, they depend on the physics at the horizon and have been proven to be tightly related to the existence of a hidden symmetry structure in general relativity. The overarching goal of my program is to advance our understanding of the tidal response and Love numbers of black holes and compact objects in two main directions: the nonlinear response and the dynamical (i.e., nonstatic) regime. We will answer in particular the questions: What is the nonlinear response of a black hole under an external tidal perturbation? Are the recently discovered symmetries that are responsible for the vanishing of the linear Love numbers an "accident" of linear response theory or, do they admit a completion to all orders in general relativity? How do the symmetries get modified in the presence of nonstatic tides? Answering these questions will have important implications for our theoretical understanding of the fundamental properties of gravity in the strong-field regime and the symmetry structure of gravitational effective field theories, which we will be able to probe with future detectors.