The electrostatic potential V(r) that is created in the space around a molecule by its nuclei and electrons is a rigorously defined property that is useful in analyzing and predicting the reactive behavior of molecules, and the study of biological recognition processes, such as drug-receptor and enzyme-substrate interactions. The chapter discusses methodology as related to both types of applications of the potential, and then focuses on a study in the area of molecular recognition involving the analysis of the electrostatic potentials of dibenzo-p-dioxins and structurally similar molecules. Dibenzo-p-dioxin(I) is the parent compound of a large family of derivatives, having halogens and other substituents at various positions. Considering only chlorine as a substituent, there are seventy-five possible derivatives of I. When bromine, fluorine, and other types of substituent groups are taken into account, there are clearly hundreds of possibilities. These have varying degrees of toxicity, ranging from virtually none to very high; the latter is exemplified by the notorious 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD, II).