The advancement of migrant-sensitive health care in Europe has been a topic of many initiatives and academics debates for over 20 years in Europe, yet with rather limited progress in terms of comprehensive and sustainable implementation. We argue that a human rights-based approach with clearly defined duties and responsibilities of governments, relevant public and private institutions as well as professionals is needed, in line with a sound understanding and thoughtful implementation and further development of concepts and standards for providing migrant sensitive care as an essential component of Universal Health Coverage. We suggest drawing particular attention to the interrelated features of accessibility, acceptability, quality, and trust to inform policies and practice. Innovative approaches with substantial involvement of social and cultural sciences are needed for adapting clinical care and health services to the growing social and cultural diversity of European societies.