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This paper describes different types of models for the evolution of communication and language. It uses the distinction between signals, symbols, and words for the analysis of evolutionary models of language. In particular, it shows how evolutionary computation techniques such as artificial life can be used to study the emergence of syntax and symbols from simple communication signals. Initially, a computational model that evolves repertoires of isolated signal is presented. This study has simulated the emergence of signals for naming foods in a population of foragers. This type of model studies communication systems based on simple signal-object associations. Subsequently, models that study the emergence of grounded symbols are discussed in general, including a detailed description of a work on the evolution of simple syntactic rules. This model focuses on the emergence of symbol-symbol relationships in evolved languages. Finally, computational models of syntax acquisition and evolution are discussed. These different types of computational models provide an operational definition of the signal/symbol/word distinction. The simulation and analysis of these types of models will help to understand the role of symbols and symbol acquisition in the origin of language