Fluid-conveying pipes are widely used to transfer bulk fluids from one point to another in many engineering applications. They are subject to various excitations from the conveying fluids, the supporting structures, and the working environment, and thus are prone to vibrations such as flow-induced vibrations and acoustic-induced vibrations. Vibrations can generate variable dynamic stress and large deformation on fluid-conveying pipes, leading to vibration-induced fatigue and damage on the pipes, or even leading to failure of the entire piping system and catastrophic accidents. Therefore, the vibration control of fluid-conveying pipes is essential to ensure the integrity and safety of pipeline systems, and has attracted considerable attention from both researchers and engineers. The present paper aims to provide an extensive review of the state-of-the-art research on the vibration control of fluid-conveying pipes. The vibration analysis of fluid-conveying pipes is briefly discussed to show some key issues involved in the vibration analysis. Then, the research progress on the vibration control of fluid-conveying pipes is reviewed from four aspects in terms of passive control, active vibration control, semi-active vibration control, and structural optimization design for vibration reduction. Furthermore, the main results of existing research on the vibration control of fluid-conveying pipes are summarized, and future promising research directions are recommended to address the current research gaps. This paper contributes to the understanding of vibration control of fluid-conveying pipes, and will help the research work on the vibration control of fluid-conveying pipes attract more attention.