Human history has been shaped by people moving to live in new places. The numbers of people living outside their countries of birth in today's societies are, however, much higher than in the past. In the European Union (EU) Member States, the number of people with citizenship of a non-member country on 1 January 2017 was 21.6 million, and there were 16.9 million persons with the citizenship of another EU Member State (Eurostat, 2018c). Among this broad group of migrants, asylum seekers and refugees, who have been obliged to leave their country, make up a relatively small percentage. However the rapid increase in numbers of asylum seekers entering Europe in the years 2015 and 2016 -- largely as a result of the conflict in Syria -- lead media and politicians to characterise the phenomenon as a migration or refugee crisis. This report was planned in the wake of this phenomenon. The President of the European Commission, Jean-Claude Juncker, in his State of the Union address in September 2015 stated that 'the first priority today is and must be addressing the refugee crisis' (European Commission 2015, p. 6). While there has been enormous political attention to the way in which the situation has been addressed, one of the areas of public policy that clearly has a role to play is higher education. In particular, a high proportion of refugees are aged in the typical higher education population range (18-34) and among these a considerable number have been enrolled in higher education programmes in their home country. While there is inevitably a strong potential demand for higher education among the refugee population, it cannot be taken for granted that this demand can be easily met. In many cases, there will be a need for potential students to learn the host country language and to adapt to the higher education system. This requires adequate information and guidance, as well as provision of adapted preparatory programmes. Refugees are also likely to be in need of considerable support -- both psychological and financial. Meanwhile for the host country, there will be a need to assess and recognise learning that cannot be demonstrated through certificates. This also requires system-level planning and action. The aim of this report is to assess how far national systems have developed in terms of being able to respond to the needs of asylum seekers and refugees.