Social science researchers are facing new challenges in data archiving and sharing. The challenges encountered for video data are different from those encountered for other types of qualitative data. I will consider these challenges with respect to the moral, pragmatic, and substantial arguments with which funding bodies justify data archiving and sharing. Throughout the article, I will draw on a recent Economic and Social Research Council funded project, “Transient Teams in the Operating Theatre,” in which our research team video recorded work activities in the operating theatre of a UK hospital, thereby dealing with highly sensitive footage. I will consider how video data, on most occasions, cannot be archived for re-use by the wider research community, but how new avenues could be developed so as to benefit from further research on such “unarchivable” datasets.