The construction of large-volume detectors of high energy, greater than 1 TeV, neutrinos is mainly driven by the search for extragalactic neutrino sources. The existence of such sources is implied by the observations of ultra-high-energy, greater than or equal to 10 19 eV, cosmic rays, the origin of which is a mystery. In this lecture, I briefly discuss the expected extragalactic neutrino signal and the current state of the experimental efforts. Neutrino emission from gamma-ray bursts (GRBs), which are probably sources of both high-energy protons and neutrinos, is discussed in some detail. The detection of the predicted GRB neutrino signal, which may become possible in the coming few years, will allow one to identify the sources of ultra-high-energy cosmic rays and to resolve open questions related to the underlying physics of GRB models. Moreover, detection of GRB neutrinos will allow one to test for neutrino properties (e.g. flavour oscillations and coupling to gravity) with an accuracy many orders of magnitude better than is currently possible.