Recent achievements have been analysed in designing and application of shape memory alloys as high-damping elements, utilizing pseudoelastic hysteresis, transient damping effects in the two-phase state and damping capacity of the martensitic phase.Dealing with intrinsic damping capacity of martensitic phases, several new observations are described, like 'universal' low-temperature high-damping properties of ternary Cu-based alloys, high non-linear damping capacity of a binary NiTi in R phase and high linear damping of binary hydrogen-charged NiTi. Based on the analysis of results of recent studies of damping in NiTi (B19 martensite, R phase) and Cu-based families of alloys (Cu-Al-Ni, Cu-Zn-Al, Cu-Al-Be), we try to introduce a guideline relating desired damping properties of a SMA with its structural characteristics. Among the parameters determining the contribution of specific defect species to damping we suggest considering• density of specific type of defects (intervariant boundaries and internal defects of variants like dislocations and twins); • their mobility (determined by crystallography and geometrical factors, like accommodation and size of martensitic variants); • concentration and type of obstacles impeding the motion of defect species and, thus, producing damping (concentration, mobility and distribution of quenched-in/point-like defects, precipitates, etc).The importance of distinguishing linear and non-linear components of damping is emphasized, since, in a general case, they can be related to different elements of defect microstructure of martensite.