The article presents a review of European and Russian studies on the perceptions of the host society towards the integration of migrants. The review demonstrates the diversity of works in this field, including both qualitative and quantitative research, as well as studies focusing on theoretical and applied developments. The article describes research that pays attention to both the general understanding of integration by local residents and its specific aspects. In the conclusions, the authors argue that hierarchies of migrants exist both in Europe and in Russia, corresponding to perceptions of their "readiness for integration." The least prepared to live "together with us" are seen as carriers of norms prevalent in the Islamic East, but these barriers are permeable. The review study shows that the strategy of adapting migrants to the standards of the majority remains popular among the local population. Nonetheless, both in Europe (to the greater extent) and in Russia there are the part of population that is ready for the integration as a process of mutual acceptance and gradual change. “Unpreparedness of integration” of the Eastern-born immigrants is explained not by their religious identity, but rather the existing social norms, which are able to gradually transform. The factors that affect this transformation are not just contacts (deliberate or not), but also the inclusion both locals and immigrants in the collective search for solution to the problems relevant to both groups. Otherwise, the participants of the integration activities do not consider them as necessary or important, meaning that the integration does not occur despite the contacts existence.