Human language is learned, symbolic and exhibits syntactic structure, a set of properties which make it unique among naturally-occurring communication systems. How did human language come to be as it is? Language is culturally transmitted and cultural processes may have played a role in shaping language. However, it has been suggested that the cultural transmission oflanguage is constrained by some language-specific innate endowment. The primary objective of the research outlined in this paper is to investigate how such an endowment would influence the acquisition of langage and the dynamics of the repeated cultural transmission of language. To this end, a new connectionist model of the cultural evolution of communication is presented. In this model an individual's innate endowment is considered to be a learning rule with an associated learning bias. The model allows manipulations to be made to this learning apparatus andthe impact of such manipulations on the processes of language acquisition and language evolution to be explored. These investigations reveal that an innate endowment consisting of an ability to read the communicative intentions of others and a bias towards acquiring one-to-one mappings between meanings and signals results in the emergence, through purely cultural processes, of optimal communication. It has previously been suggested that humans possess just such an innate endowment. Properties of human language may therefore best be explained in terms of cultural evolution on an innate substrate.