There are clear benefits from genomics and health data sharing in research and in therapy for individuals across societies. At the same time, citizens have different expectations and fears about that data sharing. International legislation in relation with research ethics and practice and, particularly, data protection create a particular environment that, as is seen in the articles in part two of this special issue, are crying out for harmonisation both at a procedural but at fundamental conceptual levels. The law of data sharing is pulling in different directions. This paper poses the question, 'harmonisation, an impossible dream?' and the answer is a qualified 'no'. The paper reflects on what can be seen in the papers in part two of the special issue. It then identifies three major areas of conceptual uncertainty in the new EU General Data Protection Regulation (not because it has superiority over other jurisdictions, but because it is a recent revision of data protection law that leaves universal conceptual questions unclear). Thereafter, the potential for Artificial Intelligence to meet some of the shortcomings is discussed. The paper ends with a consideration of the conditions under which data sharing harmonisation might be achieved: an understanding of a human rights approach and citizen sensitivities in considering the 'public interest'; social liberalism as a basis of solidarity; and the profession of 'researcher'.