Many material systems show fascinating microstructures on different length scales in response to applied strains, stresses, or electromagnetic fields. They are at the heart of often surprising mechanical properties of the materials and a lot of research has been directed towards the understanding of the underlying mechanisms. In this text, we focus on two particular systems, shape memory materials and nematic elastomers, which display similar
microstructures, see Figure 1.1, despite being completely different in nature. The reason for this remarkable fact is that the oscillations in the state variables are triggered by the same principle: breaking of symmetry associated with solid to solid phase transitions. In the first system we find an austenite-martensite transition, while the second system possesses an isotropic to nematic transition.