The paper aims to analyze the ongoing situation in the European Union member countries caused by modern migration flows. It shows the real impact of refugees and migrants on European demography. It describes the future scenarios of global demographic and social challenges, which lead to the socio-economic and political crisis, and the failure of European political elites. The study mainly is based on the following research methods: descriptive, statistical, and analysis. The basis of the source represents the books, scientific articles, empirical and press materials, documents published on official websites in the field of migration policy. The essence of the modern migration in Europe became very acute since the current migrants are mostly followers of Islam, which in all its aspects and completeness is currently one of the most urgent topics, and draws the special attention of political circles and international clubs. Muslims in Europe are, first, immigrants whose influx into the European continent has seriously changed its demographic picture and political situation. In this regard, it should be said that the growing number of Muslims in Europe is causing certain demographic challenges that significantly affect the European socio-cultural situation, and lead to the financial and political crisis.