  Kilometer-scale neutrino detectors such as IceCube are discovery instruments
covering nuclear and particle physics, cosmology and astronomy. Examples of
their multidisciplinary missions include the search for the particle nature of
dark matter and for additional small dimensions of space. In the end, their
conceptual design is very much anchored to the observational fact that Nature
accelerates protons and photons to energies in excess of $10^{20}$ and
$10^{13}$ eV, respectively. The cosmic ray connection sets the scale of cosmic
neutrino fluxes. In this context, we discuss the first results of the completed
AMANDA detector and the reach of its extension, IceCube. Similar experiments
are under construction in the Mediterranean. Neutrino astronomy is also
expanding in new directions with efforts to detect air showers, acoustic and
radio signals initiated by super-EeV neutrinos.
