Inertial confinement fusion driven by beams of heavy ions is an attractive route to controlled fusion. In the U.S., induction accelerators are being developed as ‘‘drivers’’ for this process. This paper is divided into two main sections. In the first section, the concept of induction‐accelerator driven heavy‐ion fusion is briefly reviewed, and the U.S. program of experiments and theoretical investigations is described. In the second, a ‘‘taxonomy’’ of space‐charge‐dominated beam physics issues is presented, accompanied by a brief discussion of each area. ©1996 American Institute of Physics.