The production and acceleration of Radioactive Ion Beams (RIBs) is today an area of intense interest. The history and development of RIB facilities in Europe is presented, with discussion of both the "in-flight" and "ISOL" methods used at different laboratories. The current status of present developments like the SPIRAL II facility at GANIL and the FAIR in-flight facility at GSI are briefly reviewed. Particular emphasis is given to the recent EURISOL Feasibility Study for a European ISOL facility, and the present EURISOL Design Study.