A rapidly growing body of research examines the relationship between migration and institutions. Three strands of studies can be distinguished. Some studies focused on the role of domestic and foreign institutions in the decision to migrate. Others were interested by the impact of migration on institutional reforms in migrants' countries of origin. While the effect of migration on destination countries is largely documented, recent studies focus on how migrants affect social and informal institutions in the destination countries. This survey puts together these three strands of literature with three purposes. First, we offer a short definition and synthetic typology of institutions, which provide a guide to understand several studies summarized and their results. Second, our analysis is presented following the analytic framework exit,voice and loyalty of Hirschman in order to highlight the brain grain phenomenon for developing countries, from an institutional point of view. Third, we review the limited existing work on the very timely topic, whether migrants are harmful or not to institutions in the host countries.