Electron cooling: 35 years of development

The electron cooling technique for shrinking ion beams of extremely high phase-space density was proposed and first tested at the Nuclear Physics Institute of the Siberian Branch of the Russian Academy of Sciences. The present review traces the history of the development of the idea from its first emergence in 1965 and the discussion originated in G I Budker's talk at the symposium on electron – positron rings in Sacle in September 1966 — through 35 years of research — down to the present time, with numerous applications in many acceleration centers around the world.