When a conductive material is subjected to a time-varying magnetic flux, eddy currents are generated in the conductor. These eddy currents circulate inside the conductor generating a magnetic field of opposite polarity as the applied magnetic field. The interaction of the two magnetic fields causes a force that resists the change in magnetic flux. However, due to the internal resistance of the conductive material, the eddy currents will be dissipated into heat and the force will die out. As the eddy currents are dissipated, energy is removed from the system, thus producing a damping effect. There are several different methods of inducing a time-varying magnetic field, and from each method arises the potential for a different type of damping system. Therefore, the research into eddy current and magnetic damping mechanisms has led to a diverse range of dampers, many of which are detailed in this paper. The majority of the research in eddy current damping has taken place in the area of magnetic braking. A second topic that has received significant interest is the use of eddy current dampers for the suppression of structural vibrations. However, much of this research is not concentrated in one area, but has been applied to a variety of different structural systems in a number of distinct ways. In this paper, we review the research into various types of eddy current damping mechanisms and we discuss the future of eddy currents with some potential uses that have not yet been studied.