We review the rationale for building kilometer-scale neutrino detectors and briefly describe the first such instrument, IceCube. It has transformed one cubic kilometer of natural Antarctic ice into a Cherenkov detector that maps the light patterns radiated by the secondary particles produced in neutrino interactions. We discuss the discovery of cosmic neutrinos and reappraise the properties of the flux after the recent doubling of the data from two to four years. We conclude that the flux is isotropic with a flavor composition of 1:1:1 and therefore most likely extragalactic in origin. It is large by any measure and consistent with a neutrino flux from sources that release a similar amount of energy in photons and, possibly, cosmic rays. Strikingly, the photon flux accompanying IceCube neutrinos is, after cascading through the extragalactic background light, consistent with the high-energy gamma-ray flux observed by Fermi. This observation suggests common sources, which should ease the task of identifying the cosmic accelerators producing IceCube neutrinos. We will argue that event rates of hundreds rather than tens per year are desirable for launching a new era of astronomy. Building a detector that instruments ten cubic kilometers of ice is realistic and, as a result of the large absorption length of the ice revealed by IceCube, comparable in scope to the original project.