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Peer-to-Peer (P2P) media streaming networks, motivated by the huge success of P2P file downloading networks, have recently attracted a lot of research interest. However, it is challenging to design P2P media streaming networks because of the stringent time constraints on the delivered media streams, which require more efficient and resilient overlay architectures. In this paper, we focus on live P2P media streaming networks, a promising application flourishing in the Internet and which requires the distribution of live (not stored) multimedia content to subscribers. We review the architectures for live P2P media streaming networks, and consider both overlay topologies and their construction.