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Mobility management needs to meet the requirements of existing and emerging network technologies and applications. It may be supported in different layers of the network protocol stack. At the IP layer, Mobile IP, an IP-based mobility management, has the advantage of being applicable in any IP-based network, but is faced with many deployment challenges. Numerous variants of Mobile IP have been proposed to address these challenges in different network environments. Research in mobility management has become more active, especially with the mobile networks continuing to evolve from hierarchical towards more flattened network and densification of wireless networks. This talk presents the basics, recent advances, and future directions for mobility protocols at various layers (e.g., network, transport and application). This talk then provides taxonomy of existing mobility protocols, illustrates an abstract mobility model that can be used to support various handoff scenarios. Various handoff optimization methodologies will be explained supported by experimental and simulation results. This talk cites a few deployment scenarios to describe applicability of mobility protocols to various network environments. Many of the systems optimization techniques and mobility models discussed here can be used to provide seamless handoff support for 5G networks. 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