Tidal Love numbers quantify the finite-size properties of compact objects, such as absorption and their response to external fields. Perhaps surprisingly, even in classical general relativity, they undergo renormalization group running due to nonlinearities. In this talk I will explain some exact results about their running, which can be extracted using scattering amplitudes in black-hole perturbation theory and point-particle effective theories (EFT). Due to the universality of the EFT, the results have applications to the physics of black holes, neutron stars, binaries and their signals in gravitational wave observatories. Our calculations can also provide the precise values of both static and dynamical Love numbers of black holes in various dimensions.