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Optical networks are poised to dominate the access network space in coming years. Ethernet passive optical networks, which leverage the ubiquity of Ethernet at subscriber locations, seem destined for success in the optical access network. In this article we first provide a brief introduction to Ethernet passive optical networks, followed by a discussion of the problem of dynamic bandwidth allocation. We then introduce a framework for classifying dynamic bandwidth allocation schemes and provide a comprehensive survey of the dynamic bandwidth allocation methods proposed to date. We conclude with a side by side comparison of the schemes based on their most prominent characteristics, and outline future developments of dynamic bandwidth allocation schemes.