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This article outlines the challenges of IP multicast over Mobile IP. Then it provides a comprehensive overview of existing multicast solutions to handle mobile sources and receivers in both the Mobile IPv4 and the Mobile IPv6 environments. The solutions are classified into different classes in light of how the network infrastructure is used and the nature of the multicast members (receivers or sources). For each solution, we present a brief overview; we describe the architecture and the proposed protocol; we discuss the advantages and the limitations; and we compare qualitatively all the solutions of each class based on common criteria such as optimal routing, join latency, handover transparency, etc.