Research funding in recent years often comes with the condition to make the resulting data openly available. Just opening up research data is not enough: the data should also be of sufficient quality. In this presentation, I will propose criteria and methods to assess the quality of data sets. Part of the quality assurance can be guaranteed by digital repositories that archive and provide access to data. I will argue that the certification criteria of digital archives and the FAIR data principles for data sets provide a good basis for guaranteeing the quality or “fitness for use” of research data sets. The core certification offered by the Data Seal of Approval (DSA) and World Data System (WDS) for data repositories, in combination with the FAIR data principles get as close as possible to giving quality criteria for research data. They do not do this by trying to make value judgements about the content of datasets, but rather by qualifying the fitness for data reuse in an impartial and measurable way. By bringing the ideas of the DSA/WDS and FAIR together, we will be able to offer an operationalization that can be implemented in any certified Trustworthy Digital Repository. In 2014 the FAIR Guiding Principles (Findable, Accessible, Interoperable and Reusable) were formulated. The well-chosen FAIR acronym is highly attractive: it is one of these ideas that almost automatically get stuck in your mind once you have heard it. In a relatively short term, the FAIR data principles have been adopted by many stakeholder groups, including research funders. The FAIR principles are remarkably similar to the underlying principles of the DSA, which date back to 2005: these specify that the data can be found on the Internet, are accessible (having clear rights and licenses), are in a usable format, are reliable, and are identified in a unique and persistent way so that they can be referred to. Essentially, the DSA presents quality criteria for digital repositories, whereas the FAIR principles target individual datasets.