Induction acceleration is one of two principal approaches for producing ion beams for heavy-ion inertial fusion. This approach was first suggested by the late Denis Keefe of Lawrence Berkeley Laboratory and is the main approach of the U.S. heavy-ion-fusion program. Induction accelerators have the ability to handle high beam currents; therefore, accumulation rings or storage rings are not required. This paper reviews the target and accelerator considerations theftare important for the design of induction accelerators for fusion. These considerations, including some important assumptions, have led to a standard induction accelerator concept; however, a careful examination of the assumptions and considerations shows that many of them are not truly fundamental. Through improvements in technology, changes in design, and alternate ways of focusing beams, it appears possible to circumvent or relax the constraints imposed by the standard orthodoxy. If it is possible, it will lead to induction accelerators that are more efficient and less costly than the standard concept.