[en] Inertial fusion target physics imposes important constraints on the design of linacs for heavy-ion fusion. The most challenging constraint from a scientific standpoint is the requirement that the accelerator deliver more than 10¹⁴ W of beam power to a small quantity (less than 100 mg) of matter. The most challenging constraint from an engineering standpoint is accelerator cost. This paper explains the target physics requirements and shows how they lead to constraints on the usual accelerator parameters such as kinetic energy, current, and emittance. It will be shown that improvements in the final focusing system would have a beneficial effect on both scientific feasibility and cost. The paper also discusses experiments that are presently underway in the United States, specifically, experiments on high-current injectors, recirculating induction accelerators, transverse beam combining, and a proposed accelerator called ILSE. Hardware development for ILSE is now in progress