Shear transformations, such as deformation twinning, pseudotwinning, and martensites, can result in predictable and reversible rearrangements of the local atomic environments and the crystal symmetries. By manipulating the composition and local order of the parent phase, a degree of control can be achieved over the structure of the sheared phase. Unusual crystal structures can be created with interesting implications for thermochemical, mechanical and physical properties, and alloy theory.