Non-zero neutrino masses provide the strongest evidence for physics beyond the Standard Model of particle physics. Large neutrino detectors and cosmological observations provide more and more information about neutrino masses and mixing angles, and might soon converge toward a self-consistent description with precisely measured parameters. The origin of neutrino masses remains mysterious, however, with a seemingly unlimited number of possible models flooding the literature. I will discuss ways to potentially distinguish certain classes of models and how to render a neutrino-mass theory predictive by connecting it to other anomalous observables such as the muon’s magnetic moment or CDF’s W-boson mass.