The new radioactive beam accelerator facilities are opening exciting new opportunities to study exotic nuclei that exhibit new and radically different manifestations of nuclear matter. There are two classes of exotic beam accelerator facilities for creating beams of radioactive nuclei, fragmentation of fast ions and . Fragmentation of fast ions is one powerful approach that is being exploited extensively at the NSCL facility at Michigan State University. The Isotope Separator On-Line, ISOL, facilities separate the radioactive ions of interest from reactions products produced by a primary beam, or from a fission source, followed by acceleration by a secondary heavy-ion accelerator. In North America the primary ISOL facilities in operation, or near to operation, are HRIBF at Oak Ridge, CARIBU/ATLAS at Argonne, and ISACII at TRIUMF. The proposed Rare Isotope Accelerator facility, RIA, will be a more powerful facility that hopefully will be built in the USA during the next decade.