In Europe, the monitoring and management of migration flows are high on the political agenda. Evidence-based monitoring calls for adequate data, which do not exist. The sources of data on international migration differ significantly between countries in Europe and the initiatives to improve data collection and produce comparable data, including new legislation, did not yield the expected outcome. Scientists have developed statistical models that combine quantitative and qualitative data from different sources to derive at estimates of migration flows that account for differences in definition, undercoverage, undercount and other measurement problems. Official statisticians are reluctant to substitute estimates for measurements. This article reviews the progress made over the last decades and the challenges that remain. It concludes with several recommendations for better international migration data/estimates. They range from improved cooperation between actors to innovation in data collection and modelling.