The IceCube observatory is currently being contructed at the South Pole. Scheduled to be completed in 2011, it already offers a large increase in sensitivity over its predecessor, the AMANDA detector. This increase is expected to improve significantly the search for extraterrestrial neutrinos which are currently under way. One of the key searches at the IceCube observatory is for a diffuse flux of high energy extraterrestrial muon neutrinos, in excess of that observed from cosmic-ray induced atmospheric neutrinos. In this paper, we will review results obtained with the AMANDA and early IceCube detectors as well as give an outlook on upcoming analyses.