All high-power ion cyclotron range of frequency (ICRF) heating systems include devices for matching the input impedance of the antenna array to the generator output impedance. For most types of antennas used, the input impedance is strongly time dependent on timescales as rapid as 10-4 s, while the radio frequency (RF) generators used are capable of producing full power only into a stationary load impedance. Hence, the dynamic response of the matching method is of great practical importance. In this paper, world-wide developments in this field over the past decade are reviewed. These techniques may be divided into several classes. The edge plasma parameters that determine the antenna array's input impedance may be controlled to maintain a fixed load impedance. The frequency of the RF source can be feedback controlled to compensate for changes in the edge plasma conditions, or fast variable tuning elements in the transmission line between the generator output and the antenna input connections can provide the necessary time-varying impedance transformation. In `lossy passive schemes', reflected power due to the time-varying impedance of the antenna array is diverted to a dummy load. Each of these techniques can be applied to a pre-existing antenna system. If a new antenna is to be designed, recent advances allow the antenna array to have the intrinsic property of presenting a constant load to the feeding transmission lines despite the varying load seen by each antenna in the array.