The text discuses importance of migration in contemporary world and the transformation of the migration as a process. The author provides theoretical background, describes the reasons for migration and its character as well as problems that source countries and the countries receiving immigration have to face. Moreover, black economy related to the migration, as human trafficking, is also analyzed as well as the problems migration poses for political systems of liberal nation states. The text focuses on the immigration from Muslim countries, its characteristics and consequences for particular states and the EU as a whole. Finally, the paper analyses actions undertaken by the EU and its member states that are aimed at limiting and shaping of immigration.