Kilometer-scale neutrino detectors such as IceCube are discovery instruments covering nuclear and partile physics, cosmology and astronomy. Examples of their multidisciplinary mission include the search for the particle nature of dark matter and for additional small dimensions of space. In these lectures, we discuss the nature of cosmic neutrinos and their sources, the need for kilometer-scale detectors and the status and methodologies of current detectors.

49 pages, 9 figures. Lectures presented at the International WE Heraeus Summer School on Physics with Cosmic Accelerators