Our ability to generate genomic data is currently well ahead of our ability to understand what they mean, raising challenges about how best to engage with them. This article considers ethical aspects of work with such data, focussing on research contexts that are intertwined with clinical care. We discuss the identifying nature of genomic data, the medical information intrinsic within them, and their linking of people within a biological family. We go on to consider what this means for consent, the (...) importance of thoughtful sharing of genomic data, the challenge of constructing meaningful findings, and the legacy of unequal representation in genomic datasets. We argue that the ongoing success of genomic data research relies on public trust in the enterprise: to justify this trust, we need to ensure robust stewarding, and wide engagement about the ethical issues inherent in such practices. (shrink)