The origin of neutrinos' absurdly tiny masses and their Majorana nature remain outstanding mysteries of nature, with far-reaching consequences for astrophysics, cosmology, nuclear physics, and particle physics. In this short talk, I give a brief introduction to models that can resolve these questions, their connections and synergies to other fields, and finally what experiments like the Large Hadron Colliders can tell us about the nature of neutrinos. The latest results from ATLAS and CMS will be summarized.