  Elastic interactions arising from a difference of lattice spacing between two
coherent phases can have a strong influence on the phase separation
(coarsening) of alloys. If the elastic moduli are different in the two phases,
the elastic interactions may accelerate, slow down or even stop the phase
separation process. If the material is elastically anisotropic, the
precipitates can be shaped like plates or needles instead of spheres and can
form regular precipitate superlattices. Tensions or compressions applied
externally to the specimen may have a strong effect on the shapes and
arrangement of the precipitates. In this paper, we review the main theoretical
approaches that have been used to model these effects and we relate them to
experimental observations. The theoretical approaches considered are (i)
`macroscopic' models treating the two phases as elastic media separated by a
sharp interface (ii) `mesoscopic' models in which the concentration varies
continuously across the interface (iii) `microscopic' models which use the
positions of individual atoms.
