Research in language evolution is concerned with the question of how complex linguistic structures can emerge from the interactions between many communicating individuals. Thus it complements psycholinguistics, which investigates the processes involved in individual adult language processing, and child language development studies, which investigate how children learn a given (fixed) language. We focus on the framework of language games and argue that they offer a fresh and formal perspective on many current debates in cognitive science, including those on the synchronic-versus-diachronic perspective on language, the embodiment and situatedness of language and cognition, and the self-organization of linguistic patterns. We present a measure for the quality of a lexicon in a population, and derive four characteristics of the optimal lexicon: specificity, coherence, distinctiveness, and regularity. We present a model of lexical dynamics that shows the spontaneous emergence of these characteristics in a distributed population of individuals that incorporate embodiment constraints. Finally, we discuss how research in cognitive science could contribute to improving existing language game models.