The origin of high-energy cosmic rays, and their behavior in astrophysical sources, remains an open question. Recently, new ways to address this question have been made possible by the observation of a new astrophysical messenger, namely neutrinos. The IceCube telescope has detected a diffuse flux of astrophysical neutrinos in the TeV-PeV energy range, likely produced in astrophysical sources accelerating cosmic rays, and more recently it has reported on a few candidate individual neutrino sources. Future experiments will be able to improve on these measurements quantitatively, by the detection of more events, and qualitatively, by extending the measurement into the EeV energy range. In this paper, we review the main features of the neutrino emission and sources observed by IceCube, as well as the main candidate sources that could contribute to the diffuse neutrino flux. As a parallel question, we review the status of high-energy neutrinos as a probe of Beyond the Standard Model physics coupling to the neutrino sector.