The study of language evolution, and human cognitive evolution more generally, has often been ridiculed as unscientific, but in fact it differs little from many other disciplines that investigate past events, such as geology or cosmology. Well-crafted models of language evolution make numerous testable hypotheses, and if the principles of strong inference (simultaneous testing of multiple plausible hypotheses) are adopted, there is an increasing amount of relevant data allowing empirical evaluation of such models. The articles in this special issue provide a concise overview of current models of language evolution, emphasizing the testable predictions that they make, along with overviews of the many sources of data available to test them (emphasizing comparative, neural, and genetic data). The key challenge facing the study of language evolution is not a lack of data, but rather a weak commitment to hypothesistesting approaches and strong inference, exacerbated by the broad and highly interdisciplinary nature of the relevant data. This introduction offers an overview of the field, and a summary of what needed to evolve to provide our species with language-ready brains. It then briefly discusses different contemporary models of language evolution, followed by an overview of different sources of data to test these models. I conclude with my own multistage model of how different components of language could have evolved.