Shape memory alloys transform at low temperature by a martensitic reaction beta --> alpha, which implies formation of a domain structure (similar to ferromagnetic, ferroelectric transformations). This microstructure allows complex pseudo-plastic deformability (high degree of freedom). Reversion of (x into P restores a definite shape, either by heating to T > A(f) (austenite finish), or by reduction of the external transformational stress (pseudo-elasticity). It is discussed how a defined final shape is achieved at temperatures high above Af, at which diffusional processes can take place. In addition maximum strength is required for many SMA applications,- especially a high stability at repeated transformations (fatigue, loss of memory). The origin of the microstructure is discussed, which leads to the desired combination of properties. Special attention is paid to then-no-mechanical treatments (TMT), by which a wide range of microstructures can be obtained. A systematic approach is provided for the types of reverse reactions cc -), P, which are found between, crystalographically reversible (martensitic) and diffusion controlled (combined reactions). Features of optimum microstructures for shaping and desired SM-properties are discussed.