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This kind of research is performed in a variety of traditions including language evolution, developmental psychology, cognitive science, artificial intelligence, and robotics. The motivations for the models are different, but the operationalisations and methods used are often similar. We identify the assumptions and explanatory targets of the most representative models and summarise the known results. We claim that some of the assumptions\u2014such as portraying meaning in terms of mapping, focusing on the descriptive function of communication, and modelling signals with amodal tokens\u2014may hinder the success of modelling. Relaxing these assumptions and foregrounding the interactions of embodied and situated agents allows one to systematise the multiplicity of pressures under which symbolic systems evolve. 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