Biobanks and archived datasets collecting samples and data have become crucial engines of genetic and genomic research. Unresolved, however, is what responsibilities biobanks should shoulder to manage incidental findings (IFs) and individual research results (IRRs) of potential health, reproductive, or personal importance to individual contributors (using “biobank” here to refer to both collections of samples and collections of data). This paper reports recommendations from a 2-year, NIH-funded project. The authors analyze responsibilities to manage return of IFs and IRRs in a biobank research system (primary research or collection sites, the biobank itself, and secondary research sites). They suggest that biobanks shoulder significant responsibility for seeing that the biobank research system addresses the return question explicitly. When re-identification of individual contributors is possible, the biobank should work to enable the biobank research system to discharge four core responsibilities: to (1) clarify the criteria for evaluating findings and roster of returnable findings, (2) analyze a particular finding in relation to this, (3) re-identify the individual contributor, and (4) recontact the contributor to offer the finding. The authors suggest that findings that are analytically valid, reveal an established and substantial risk of a serious health condition, and that are clinically actionable should generally be offered to consenting contributors. The paper specifies 10 concrete recommendations, addressing new biobanks and biobanks already in existence.