Asylum-related migration is highly complex, uncertain, and volatile, which precludes using standard model-based predictions to inform policy and operational decisions. At the same time, asylum’s potentially high societal impacts on receiving countries and the resource implications of asylum processes call for more proactive approaches for assessing current and future migration flows. In this article, we propose an alternative approach to asylum modeling, based on the detection of early warning signals by using models originating from statistical control theory. Our empirical analysis of several asylum flows into Europe in 2010–2016 demonstrates the approach’s utility and potential in aiding the management of mixed migration flows, while also shedding more light on the work needed to make better use of the “big data” and scenario-based methods for comprehensive and systematic examination of risk, uncertainty, and emerging trends.