The shapes, sizes, and distribution of second-phase precipitates are the principal factors determining the mechanical, electrical, and magnetic properties of a wide variety of high technology alloys. In the initial processing, and also in high temperature applications, such as jet engine superalloys, the precipitate morphologies evolve in time and the properties change. An understanding of the elastic interactions between matrix and precipitates, among the precipitates, and between precipitates and dislocations is crucial for predicting and manipulating the properties of the alloys. Therefore, there has been a need for a computational technique, through which one can analyze the elastic state associated with arbitrarily-shaped precipitates whose elastic constants are different from those of the matrix phase. This overview presents a new technique, termed the Discrete Atom Method, which is predicated upon the combination of statistical mechanics and linear elasticity. The problems treated are the elastic strain energy and morphology of a coherent precipitate, the elastic interaction between precipitates, coherency-influenced coarsening, the effects of an applied stress, and the elastic interaction between a precipitate and edge dislocations.