As anticipated in the Introduction, in recent years there has been a successful effort to use nonlinear elasticity theory, based on molecular considerations, for modelling the behavior of crystals in the range of finite deformations, like the ones encountered in mechanical twinning or in symmetrybreaking diffusionless phase transformations. These typically lead to the formation of coherent microstructures in which the phase variants mix in a great variety of configurations, and these effects are important for understanding the macroscopic behavior of materials; the latter can be very interesting also from the point of view of the applications. For instance, certain alloys exhibit shape-memory properties due to the ability of the material to form an array of self-accommodating equilibrium phase mixtures, involving periodic (patches of) twinned microstructures, in response to the imposed boundary conditions such as given loads or deformations.