For the wide variety of structural types subject to significant dynamic loads, increasingly rigorous performance requirements dictate a derivative requirement for improvements in the technologies for controlling dynamic response. Aerospace structures, subject to stringent static as well as dynamic response requirements and characterized by complex behaviors including closely spaced and often coupled modes, provide one example of a class of structures requiring improved control technologies. Similarly, for many types of civil structures --e.g., cable-stayed and suspension bridges-- also characterized by stringent performance requirements and complex structural behaviors. Control of dynamic response dictates improved design (and retrofit) approaches. Also for many mechanical systems, e.g., medical devices -- performance is constrained by limits on the control of dynamic response. In designing for dynamic loads, structural and mechanical engineers have several techniques at their disposal, including passive damping, isolation, active and semi-active control. The study presented here focuses on a novel passive damping technology based on exploiting the unique properties of shape-memory materials (SMM). SMMs are a family of materials displaying a characteristic thermoelastic phase transformation which itself is the basis of two important mechanical hystereses -- shape-memory effect (SEE) and superelastic effect (SEE). As supported by this study, SME and SEE each provides an energy dissipation mechanism with extraordinarily attractive properties for damping applications. As elaborated below, the properties of SMM damping devices include: hysteretic damping with a diversity of distinct force/deflection hysteretic behaviors highly reliable energy dissipation based on a precisely repeatable solid state phase transformation very high damping per unit mass and per unit volume of SMM material relative insensitivity to temperature variation over wide range of operating temperatures essentially zero creep over range of operating temperatures encountered in most space and all civil structures wide range of design operating temperatures excellent fatigue and corrosion resistance pure hysteretic damping --i.e., energy dissipation is frequency independent