  In this paper we review the search for astrophysical neutrinos. We begin by
summarizing the various theoretical predictions which correlate the expected
neutrino flux with data from other messengers, specifically gammas and
ultra-high energy cosmic rays. We then review the status and results of
neutrino telescopes in operation and decommissioned, the methods used for data
analysis and background discrimination. Particular attention is devoted to the
challenge enforced by the highly uncertain atmospheric muon and neutrino
backgrounds in relation to searches of diffuse neutrino fluxes. Next, we
examine the impact of existing limits on neutrino fluxes on studies of the
chemical composition of cosmic rays. After that, we show that not only do
neutrinos have the potential to discover astrophysical sources, but the huge
statistics of atmospheric muons can be a powerful tool as well. We end by
discussing the prospects for indirect detection of dark matter with neutrino
telescopes.
