Recent achievements have been analysed in designing and application of shape memoryalloys as high-damping elements, utilizing pseudoelastic hysteresis, transient dampingeffects in the two-phase state and damping capacity of the martensitic phase.Dealing with intrinsic damping capacity of martensitic phases, several newobservations are described, like ‘universal’ low-temperature high-dampingproperties of ternary Cu-based alloys, high non-linear damping capacity of abinary NiTi in R phase and high linear damping of binary hydrogen-chargedNiTi. Based on the analysis of results of recent studies of damping in NiTi(B 19′ martensite, R phase) and Cu-based families of alloys (Cu–Al–Ni, Cu–Zn–Al, Cu–Al–Be), wetry to introduce a guideline relating desired damping properties of a SMA with itsstructural characteristics. Among the parameters determining the contribution of specificdefect species to damping we suggest consideringdensity of specific type of defects (intervariant boundaries and internal defectsof variants like dislocations and twins);their mobility (determined by crystallography and geometrical factors, likeaccommodation and size of martensitic variants);concentration and type of obstacles impeding the motion of defect speciesand, thus, producing damping (concentration, mobility and distribution ofquenched-in/point-like defects, precipitates, etc).The importance of distinguishing linear and non-linear components of damping isemphasized, since, in a general case, they can be related to different elements of defectmicrostructure of martensite.