Materials science has emerged as one of the central pillars of the modern physical
sciences and engineering. A central tenet of it is that many properties of a material are
dominated by microstructures of the material. Therefore it is extremely important to study
the formation and evolution of microstructure. Some microstructure is formed by phase
transitions. We are intersted in phase transitions driven by configurational forces, in
elastically deformablesolids (e.g. Steel, Shape memory alloy). To model this kind of
phase transitions, a phase-field approach is used. We also discuss mathematical restults of
the new models.