  Neutrinos are unique cosmic messengers. Present attempts are directed to
extend the window of cosmic neutrino observation from low energies (Sun,
supernovae) to much higher energies. The aim is to study the most violent
processes in the Universe which accelerate charged particles to highest
energies, far beyond the reach of laboratory experiments on Earth. These
processes must be accompanied by the emission of neutrinos. Neutrinos are
electrically neutral and interact only weakly with ordinary matter; they thus
propagate through the Universe without absorption or deflection, pointing back
to their origin. Their feeble interaction, however, makes them extremely
difficult to detect. The years 2008-2010 have witnessed remarkable steps in
developing high energy neutrino telescopes. In 2010, the cubic-kilometre
neutrino telescope IceCube at the South Pole has been completed. In the
Mediterranean Sea the first-generation neutrino telescope ANTARES takes data
since 2008, and efforts are directed towards KM3NeT, a telescope on the scale
of several cubic kilometres. The next years will be key years for opening the
neutrino window to the high energy Universe. With an instrumented volume of a
cubic kilometre, IceCube is entering a region with realistic discovery
potential. Discoveries or non-discoveries of IceCube will have a strong impact
on the future of the field and possibly mark a "moment of truth". In this
review, we discuss the scientific case for neutrino telescopes, describe the
detection principle and its implementation in first- and second-generation
installations and finally collect the existing physics results and the
expectations for future detectors. We conclude with an outlook to alternative
detection methods, in particular for neutrinos of extremely high energies.
