Neutrino astronomy opens a new window for the observation and study of high-energy phenomena in our Universe. The emission of high energy neutrinos is intimately related to that of gamma rays and cosmic rays (CRs) via hadronic interactions in extragalactic sources or the cosmic environment. I will discuss our present expectations for the cosmogenic neutrino flux associated with the propagation of ultra-high energy (UHE) CRs in the cosmic radiation background. This flux is a "guaranteed" contribution to the diffuse EeV neutrino background but shows a strong model dependence on the UHE CR scenario. Specific models of extragalactic TeV to PeV neutrino sources are already testable by large volume neutrino observatories like IceCube. I will show how present limits on diffuse and point-source neutrino fluxes can be used to constrain candidate sources of UHE CRs like gamma ray bursts.