This contribution looks at cultural heritage institutions and their digital assets from a commons perspective. Since the beginning of digitization in the late 1990s and with the change of the medium from the analogue to the digital, the role and mission of cultural heritage institutions has changed. Challenges for managing their assets in the sense of a commons arise, on the one hand, due to the current legislation on copyright and intellectual property rights, and, on the other, because of the availability of digital cultural heritage as Big Data, which opens up possibilities for economic exploitation of these assets by private companies. Should digital assets be available open access, or should access and use be regulated? This short paper discusses the possibilities for this model of sovereign data governance within the legal regimes of intellectual property rights and the public domain.