We review the status of the IceCube observations of cosmic neutrinos. We investigate model-independent constraints on the properties of the sources where they originate. Specifically, we evaluate the multimessenger relations connecting neutrino, gamma ray, and cosmic ray observations and conclude that neutrinos are ubiquitous in the nonthermal universe, suggesting a more significant role than previously anticipated. Subsequently, we study the implications of IceCube’s upper limits on the flux from individual point sources, as well as on the “guaranteed” flux of cosmogenic neutrinos.