Even though the Standard Model has been incredibly successful, it cannot be the ultimate theory that describes the interactions among the fundamental particles. The existence of dark matter and the observation of neutrino oscillations, for instance, provide incontrovertible evidence for physics beyond the Standard Model. One of the most important open problems in particle physics today is precisely that of determining what this new physics is. In this talk I will explore tentative connections between neutrinos and dark matter that may shed light on that question.