Offshore platforms are widely used to explore, drill, produce, storage, and transport ocean resources and are usually subject to environmental loading, such as waves, winds, ice, and currents, which may lead to failure of deck facilities, fatigue failure of platforms, inefficiency of operation, and even discomfort of crews. In order to ensure reliability and safety of offshore platforms, it is of great significance to explore a proper way of suppressing vibration of offshore platforms. There are mainly three types of control schemes, i.e., passive control schemes, semi-active control schemes, and active control schemes, to deal with vibration of offshore platforms. This paper provides an overview of these schemes. Firstly, passive control schemes and several semi-active control schemes are briefly summarized. Secondly, some classical active control approaches, such as optimal control, robust control, and intelligent control, are briefly reviewed. Thirdly, recent advances of active control schemes with delayed feedback control, sliding model control, sampled-data control, and network-based control are deeply analyzed. Finally, some challenging issues are provided to guide future research directions.