This work discusses the perspectives to observe fluxes of high energy astrophysical neutrinos with the planned km3 telescopes. On the basis of the observations of GeV and TeV gamma-rays, and of ultra high energy cosmic rays, it is possible to construct well motivated predictions that indicate that the discovery of such fluxes is probable. However the range of these predictions is broad, and the very important opening of the ``neutrino window'' on the high energy universe is not guaranteed with the current design of the detectors. The problem of enlarging the detector acceptance using the same (water/ice Cherenkov) or alternative (acoustic/radio) techniques is therefore of central importance.

Proceedings of "Very Large Volume neutrino Telescopes" workshop (Catania, november 2005). 16 pages, 10 figures