In the article, an attempt to characterize migration movements observed in the beginning of the second decade of the XXI century is made. The aim is to present challenges and threats for security o f the EU region and member states, caused by massive migration flows. A debate within the European Union on possible solutions of the problem is analyzed. Differences in the approach to the migration crisis are taken into account, motivated on one hand by the desire to guarantee protection to refugees and persons in a refugee-like situation, on the other - to preserve security of EU citizens, member states and the organization.