%$Modified: Mon Apr 28 14:56:21 2003 by wgd $ Localization W. G. Dwyer This is a largely expository paper, which describes the concept of localization, as it usually comes up in topology, and gives some examples of it. The examples include local homology and cohomology, homological localizations of spaces and spectra, and localization with respect to a map f. For appropriate choices of the map f, this last gives constructions related to the Goodwillie calculus and to motivic homotopy theory. There's also a proof that if a localization functor exists, the higher order categorical invariants associated to inverting the local equivalences are trivial.