Evolutionary linguistics is the branch of linguistics that concerns itself with the evolution of language, i.e. the processes that led to the evolution of the human faculty of language. It is a multidisciplinary field involving neurolinguistics, cognitive science, anthropology and others.
Some of the core questions in evolutionary linguistics are stated on the website of the linguistics department of the University of California, Santa Barbara:
Since spoken language does not leave any fossil record, the study of the origin and evolution of language is necessarily inferential on the basis of cross-disciplinary understanding of linguistics, neuroscience, paleoanthropology, molecular genetics, and animal cognition/communication. Of particular significance are those hominid behaviors that cannot take place without linguistic communication. A surprising issue that rises from this cross-disciplinary research is the nature of language.
There are many others, as will become apparent in this article.