The growing demand for renewable energy supply stimulates a drastic increase in the deployment rate of offshore wind energy. Offshore wind power generators are usually supported by large foundation piles that are driven into the seabed with hydraulic impact hammers or vibratory devices. The pile installation process, which is key to the construction of every new wind farm, is hindered by a serious by-product: the underwater noise pollution. This paper presents a comprehensive review of the state-of-the-art computational methods to predict the underwater noise emission by the installation of foundation piles offshore including the available noise mitigation strategies. Future challenges in the field are identified under the prism of the ever-increasing size of wind turbines and the emerging pile driving technologies.