This chapter is written for a scientifically literate reader without assuming any specific background in medicine, physics, or mathematics. The chapter emphasizes that while radiation kills tumor, it also damages healthy tissue nearby. Thus, the fundamental challenge is to maximize tumor-kill while maintaining toxic effects on healthy tissue within tolerable limits. Three approaches to manage this tradeoff are described: spatial localization of radiation dose; temporal dispersion of radiation dose; and selection of an appropriate radiation modality. The optimal fractionation problem is then introduced within the context of these three approaches. The monograph relies upon the linear quadratic (LQ) framework of radiation dose response to build and solve mathematical formulations of the optimal fractionation problem. This LQ framework is recalled briefly. This chapter provides motivation for all subsequent material in the monograph. An outline of the remainder of the monograph is included at the end.