The installation of wind energy increased in the last twenty years, as its cost decreased, and it contributes to reducing GHG emissions. A race toward gigantism characterizes wind turbine development, primarily driven by offshore projects. The larger wind turbines are facing higher loads, and the imperatives of mass reduction make them more flexible. Size increase of wind turbines results in higher structural vibrations that reduce the lifetime of the components (blades, main shaft, bearings, generator, gearbox, etc.) and might lead to failure or destruction. This paper aims to present in detail the problems associated with wind turbine vibration and a thorough literature review of the different mitigation solutions. We explore the advantages, drawbacks, and challenges of the existing vibration control systems for wind turbines. These systems belong to six main categories, according to the physical principles used and how they operate to mitigate the vibrations. This paper offers a multi-criteria analysis of a vast number of systems in different phases of development, going from full-scale testing to prototype stage, experiments, research, and ideas.