This paper demonstrates that the Fukui function plays a central role in the study of chemical reactivity and selectivity. Both the Frontier Molecular Obital (FMO) Theory and the Hard-Soft-Acid-Base (HSAB) principle are intrinsically related to the Fukui function. By using an energy perturbation method within the framework of density functional theory (DFT), we have shown that the FMO theory can be understood as a part of the HSAB principle. The selectivity of a chemical reaction is determined by the nature of the reaction. Thus, for a hard reaction, the site of minimal Fukui function is preferred; for a soft reaction, the site of maximal Fukui function is preferred.