Over the last five years, there has been substantial international interest in a high luminosity (approx. 1033cm-2s-1) polarized electron-ion collider covering a CM energy range from about 30 to 100 GeV. Workshops have taken place in Europe in 1997 and in the United States at IUCF (1999), BNL (1999), Yale (2000) and MIT (2000). An Electron-Ion Collider (EIC) collaboration was formed in the fall of 2000, and in the United States, the 2001 Long Range Plan favorably endorsed the science of EIC and urged R&D support as a high priority. In March 2002, a series of workshops at BNL involving over 150 physicists from around the world agreed to produce a conceptual design of an electron-ion collider within three years. Further, it was agreed to develop this design around the existing Relativistic Heavy Ion Collider (RHIC) at BNL. This design is known as eRHIC. In this paper the scientific highlights of eRHIC are described. © 2004 American Institute of Physics [ABSTRACT FROM AUTHOR]