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Metaverse over wireless networks is an emerging use case of the sixth generation (6G) wireless systems, posing unprecedented challenges in terms of its multi-modal data transmissions with stringent latency and reliability requirements. Towards enabling this wireless metaverse, in this article we propose a novel semantic communication (SC) framework by decomposing the metaverse into human/machine agent-specific semantic multiverses (SMs). An SM stored at each agent comprises a semantic encoder and a generator, leveraging recent advances in generative artificial intelligence (AI). To improve communication efficiency, the encoder learns the semantic representations (SRs) of multi-modal data, while the generator learns how to manipulate them for locally rendering scenes and interactions in the metaverse. Since these learned SMs are biased towards local environments, their success hinges on synchronizing heterogeneous SMs in the background while communicating SRs in the foreground, turning the wireless metaverse problem into the problem of semantic multiverse communication (SMC). Based on this SMC architecture, we propose several promising algorithmic and analytic tools for modeling and designing SMC, ranging from distributed learning and multi-agent reinforcement learning (MARL) to signaling games and symbolic AI.