Biobanks and archived data sets 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 and individual research results of potential health, reproductive, or personal importance to individual contributors (using "biobank" here to refer both to collections of samples and collections of data). This article reports recommendations from a 2-year project funded by the National Institutes of Health. We analyze the responsibilities involved in managing the return of incidental findings and individual research results in a biobank research system (primary research or collection sites, the biobank itself, and secondary research sites). We suggest that biobanks shoulder significant responsibility for seeing that the biobank research system addresses the return question explicitly. When reidentification 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 the roster of returnable findings, (2) analyze a particular finding in relation to this, (3) reidentify the individual contributor, and (4) recontact the contributor to offer the finding. We suggest that findings that are analytically valid, reveal an established and substantial risk of a serious health condition, and are clinically actionable should generally be offered to consenting contributors. This article specifies 10 concrete recommendations, addressing new biobanks as well as those already in existence.