Recent interest in the use of automated or semi-automated energy dispersive X-ray fluorescence analysis has created the need for improved mathematical techniques and computer software for use with this type of analysis. The present paper reviews the efforts to date to develop the mathematical techniques necessary for implementing: (1) the library least-squares method for the determination of characteristic elemental X-ray intensities and (2) the use of the Monte Carlo method for extending the fundamental parameters approach to radioisotope and X-ray machine exciting sources for the determination of elemental amounts.