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This article surveys different resource allocation algorithms developed for the downlink of multiuser OFDM wireless communication systems. Dynamic resource allocation algorithms are categorized into two major classes: margin adaptive (MA) and rate adaptive (RA). The objective of the first class is to minimize the total transmit power with the constraint on users' data rates whereas in the second class, the objective is to maximize the total throughput with the constraints on the total transmit power as well as users' data rates. The overall performance of the algorithms are evaluated in terms of spectral efficiency and fairness. Considering the trade-off between these two features of the system, some algorithms attempt to reach the highest possible spectral efficiency while maintaining acceptable fairness in the system. Furthermore, a large number of RA algorithms considers rate proportionality among the users and hence, are categorized as RA with constrained-fairness. Following the problem formulation in each category, the discussed algorithms are described along with their simplifying assumptions that attempt to keep the performance close to optimum but significantly reduce the complexity of the problem. It is noted that no matter which optimization method is used, in both classes, the overall performance is improved with the increase in the number of users, due to multiuser diversity. Some on-going research areas are briefly discussed throughout the article.