Martensite: thousands of years applied – still not understood?

We briefly repeat some basics, i.e. what defines a martensitic phase transformation (MPT) in general, what are the characteristic features, and historic and modern applications. We then show, how a systematic order can be achieved in the broad spectrum of martensitic systems, at least the metallic ones. We discuss the physical background of the lattice instabilities and the characteristic differences – and similarities - of Fe-based systems on the one hand, and non-magnetic and ferromagnetic Hume-Rothery systems on the other hand on a microscopic length scale. We will show that the key to martensite lies in the understanding of the electronic structure of the respective materials. Phonon softening at certain q-vectors of the Brillouin Zone at temperatures above Ms is not a necessary condition for the appearance of the martensitic transition. At the end we will briefly highlight in general the shape memory behavior, the one way-, the two way-, and the magnetic shape memory-effect and briefly touch the present microscopic knowledge of these effects.