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Until recently, most data interoperability techniques involved central components, e.g., global schemas or ontologies, to overcome semantic heterogeneity for enabling transparent access to heterogeneous data sources. Today, however, with the democratization of tools facilitating knowledge elicitation in machine-process-able formats, one cannot rely on global, centralized schemas anymore as knowledge creation and consumption are getting more and more dynamic and decentralized. Peer Data Management Systems (PDMS) implementing semantic overlay networks are a good example of this new breed of systems eliminating the central semantic component and replacing it through decentralized processes of local schema alignment and query processing. As a result semantic interoperability becomes an emergent property of a self-organizing system. In this talk we provide examples of both structural and dynamic aspects of emergent semantics systems based on semantic overlay networks. From the structural perspective we can show that some of the typical properties of self-organizing networks also appear in semantic overlay networks. They form directed, scale-free graphs. We present both analytical models for characterizing those graphs and empirical results providing insight on their quantitative properties. Then we present semantic gossiping, a model for the dynamic reorganization of semantic overlay networks resulting from information propagation through the network and local realignment of semantic relationships. The techniques we apply in that context are based on belief propagation, a distributed probabilistic reasoning technique frequently encountered in self-organizing systems. Finally we will give a quick glance on how this technique can be implemented at the systems level, based on a peer-to-peer systems approach.