Computational social science provides an innovative set of methodological tools that can help answer questions of substantive interest to migration and integration research. In this introductory article, we first provide a brief history of how computational approaches have already enriched migration and integration research. Second, we identify several key promises of computational migration research (e.g. better access to hard-to-reach populations, cost reductions and time savings, better detection of causal mechanisms, avoidance of response biases and methodological nationalism through fine-grained, time-stamped, live digital trace data) and key challenges (e.g. missing categories, sampling issues, ethical concerns). Third, we illustrate how the contributions of this special issue fulfil some of these promises – as well as deal with the challenges – to gain new insights into key questions of migration and integration research that address why people emigrate, what the evolution of structural patterns in migration networks is, whether refugee movements can be predicted, how host communities respond to the influx of refugees, how people interpret, frame, and discuss these arrivals, how migration-related discourse responds to external shocks, and how spatial segregation patterns of migrants and ethnic minorities emerge.