Intensification and growth of interstate migration flows, emergence of new trends and factors influenced formation of the modern approaches to migration problems and interdisciplinary analysis of these processes. There was a transformation of the methodology and the new theories appeared. Migration processes in Europe have its specific features that have affected the conceptualization of this phenomenon. At the beginning of the article the author considers general migration theories which formed the basis of the European approaches to the migration flows, taking into consideration economic integration. The evolution of European migration theories which were based originally on American concepts and used its conclusions is analyzed in the article. Then European and American theories were merged and reformatted particularly neoclassical economic concepts and sometimes sociological so that theoretical diversity was observed. European researchers are using modified models that consider the influence of economic integration in Europe, national specifics, supranational approach to migration, appearance of Islamic factor and growth of ethno and cultural diversity in the European society. The article highlights the main trends of European migration studies - from theories of dual market, transnational migration, migration networks to concepts of migrant`s assimilation and integration, multiculturalism and interculturalism.