A high damping capacity is considered as one of the important functional properties of shape memory alloys. Those properties are related to a thermoelastic martensitic transformation. As a consequence of this transformation, the internal friction or damping can be investigated for three different states : 1. during thermal transformation cycling, 2. during martensite induced strain cycling at constant temperature, 3. in the martensitic state. The difficulty of formulating a unified theory to those three approaches is related to the complexity of the microstructure. Phase boundaries, dislocations, precipitates, impurities and point-defects interact strongly with each other, thereby influencing the macroscopic observation. However, improved models have been recently formulated to describe the observed internal friction during transformation, taking into account the change in defect mobility. This has also lead to a new approach of analyzing the observed damping in an amplitude dependent and amplitude independent part. Special attention is also given to superelastic damping with the aim of improving earthquake resistance of constructions, concentrating reversible hysteretic behaviour in detailed regions of the structure. Moreover, new relations between other functional properties and the internal friction of the martensite have been established. This paper will describe the recent findings, the importance of the results, fundamentally and practically, concurrently pointing to some interesting topics for further research