International transfers of human biological material (biospecimens) and data are increasing, and commentators are starting to raise concerns about how donor wishes are protected in such circumstances. These exchanges are generally made under contractual material transfer agreements (MTAs). This paper asks what role, if any, should research ethics committees (RECs) play in ensuring legal and ethical conduct in such exchanges. It is recommended that RECs should play a more active role in the future development of best practice MTAs involving exchange of biospecimens and data and in monitoring compliance.