  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.
