It is now one decade since serious consideration was first given to the use of heavy ion accelerators for inertial confinement fusion. After an initial period of wide-ranging studies, the US program settled on an induction linac method proposed by Lawrence Berkeley Laboratory (LBL). The ion kinetic energy is modest (30–100 MeV/amu, 5–10 GeV total) but intense beam currents of order 1 kA per beam in 10–30 beams are required on target in a short pulse of order 10–20 ns. In this review the conceptual designs are described, together with recent theory and experiments on high-current beam transport and use of multiple beams. Parallel efforts in West Germany, Japan and the Soviet Union are mentioned, and a two-year US study of heavy ion fusion electric power plants is summarized.