Tidal Love numbers quantify the deformability and dissipative properties of compact gravitating objects. However, even in classical GR, they undergo renormalization group running due to the nonlinearity of gravity. In this talk I will explain some exact results about their running, which can be extracted by matching calculations of scattering amplitudes in black hole perturbation theory and point-particle effective theories. Due to the universality of EFT, the results have applications to the physics of black holes, neutron stars, and even binary systems. For the specific case of black holes, our matching calculation also provides the precise values of both static and dynamical Love numbers in various dimensions.