The issue we address in this review paper is to what extent does mutual adaptation play a role in the emergence and evolution of phonological systems. Adaptation to the interlocutor has been shown to take many forms and to embrace all the levels of spoken language, from adjustments in vocal intensity to changes in word forms over the course of a conversational exchange, as well as lexical and syntactic alignment across speakers, to name but a few examples. Phonetic convergence, that is, the tendency for two speakers engaged in a conversational exchange to sound more like each other, is one important aspect of between-speaker adaptation. Empirical evidence has recently accumulated that shows that phonetic convergence is a recurrent phenomenon in mature speakers. This phenomenon relies on sensory-motor abilities that infants may already possess at birth. Phonetic convergence affects the way in which both speakers speak after their interaction has ended, and may build up over long periods of time. It may also be a driving mechanism in the acquisition of the phonology and phonetics of a second language. In this paper, (i) we outline the role of imitation in modern speech and language; (ii) we review the evidence provided by experimental and modelling studies for the potential role of imitation in the emergence and evolution of phonological systems; and (iii) we discuss how the resulting hypotheses could be tested in the framework provided by the multi-agent computational COSMO model.