© 2017 Human tissue biorepositories and the biospecimens they provide play a critical role in advancing research and medical care, especially in supporting research to develop precision medicine. However, advancements in genomics, informatics, and other sophisticated technologies and extensive biospecimen and data sharing have raised questions about how best to protect research participants. Complex ethical issues remain unresolved, such as the identifiability of biospecimens and associated data, the best consent models for future research, ownership and commercial use of biospecimens, and return of individual research results. This review summarizes the relevant US regulations and recent changes to them, as well as current and future ethical and policy issues related to biospecimen research. Because many issues remain unresolved, additional policy development will be needed. We discuss approaches for how researchers and other stakeholders can provide input to ensure that these policies will protect research participants while facilitating research important for scientific and medical advancements.