Vibrations in marine offshore marine structures, due to various environmental loads, can reduce platform productivity, endanger safety, affect serviceability of the structure and have been attributing factors in several major accidents and failures in the marine and offshore industry over the last few decades. Controlling the vibrations in marine offshore structures potentially due to self-excited nonlinear hydrodynamic forces, large deformations and highly nonlinear responses, is challenging. While general vibration control strategies have been investigated and demonstrated to be effective for structural vibration mitigation, there currently is limited research highlighting the specific methods available for design engineers and researchers concerned with vibrations of marine offshore structures.This paper provides a review of vibration control techniques and their application for marine offshore structures. Initially, a review of the general approaches following the conventional categorization of passive, active, semi-active and hybrid is presented. This is then followed by a review of the specific marine offshore vibration control methods and a comparison of the approaches. The marine offshore structures considered in this review include jacket structures, tension leg platforms (TLPs), spar structures, floating production storage and offloading vessels (FPSOs) and riser structures. It can be found that the general trend is progressing towards semi-active and hybrid vibration control from passive or active control, as they provide more practical approaches for implementation, possessing the advantages of passive and active control systems.