Flexible structures may experience excessive levels of vibration under the action of wind, adversely affecting serviceability and occupant comfort. To ensure the functional performance of a structure, various design modifications are possible, ranging from alternative structural systems to the utilization of passive and active control devices. This paper presents an overview of state-of-the-art measures that reduce the structural response of buildings, including a summary of recent work in aerodynamic tailoring and a discussion of auxiliary damping devices for mitigating the wind-induced motion of structures. In addition, some discussion of the application of such devices to improve structural resistance to seismic events is also presented, concluding with detailed examples of the application of auxiliary damping devices in Australia, Canada, China, Japan, and the United States.