This paper is part of the joint project between the Directorate General for Migration and Home Affairs of the European Commission and the OECD’s Directorate for Employment, Labour and Social Affairs on “Review of Labour Migration Policy in Europe”. This document has been produced with the financial assistance of the European Union. The views expressed herein can in no way be taken to reflect the official opinion of the European Union. Grant: HOME/2013/EIFX/CA/002 / 30-CE-0615920/00-38 (DI130895) A previous version of this paper was presented and discussed at the OECD Working Party on Migration in June 2015.The paper investigates the preferences and post-graduation mobility behaviour of international students, focusing on how the EU could succeed in attracting and keeping highly educated talent from across the globe. Providing their skills to European labour markets, graduates from outside the EU have a potential to enrich the supply of high-skilled labour. Seen as the 28 EU countries still constitute the most attractive destination area for studying abroad, the paper examines different calculation methods in order to generate stay rates for over 170 countries of origin. Empirical results indicate that for the EU as a whole, aggregate stay rates from stayers from all non-EU source countries lie within a range of 16.4% and 29.1%. They are also typically very low among students from other OECD countries, and much higher for students from less developed or politically less stable countries. The paper concludes by recommending a catalogue of measures to boost the EU's attractiveness, and to increase stay rates. Proposed policy measures draw on a smooth labour market integration of international graduates, as well as on cultivating strong points of the European countries, such as: political stability and participation possibilities, reliable institutions and governance structure, as well as an innovative and competitive environment.