Complex adaptive systems are all around us, and include such diverse examples as the immune system, the world economy, and the study of language. The evolution of human languages has been the most recent research activity of the Santa Fe Institute. Among the themes of this research are the search for general principles of complex adaptive systems, their broad implications, and how the study of language contributes to, and learns from, the general questions of complexity and evolution. In addition, such diverse topics as dating and origin of human language; the relationship between complexity, evolution, and the similarities and regularities in grammatical processes across language; the evolution of language universals; the phylogeny of language; the role of complexity in language change; and language acquisition by children are all explored.