Art museum curators typically aim to tell stories spanning individual artworks, thereby connecting exhibited works to each other and making exhibitions greater than the sum of their parts. For art museum visitors, however, these relations are rarely explicitly clear, while learning about them has considerable potential for improving their visiting experience. Manually considering all relations between exhibited works is infeasible, however, and automatic methods for relation exploration tend to identify many relations unlikely to be of interest for museum visitors. In this study, we took a data-driven approach to understand what makes artwork relations interesting for art museum visitors. Our contributions are as follows: 1. We create a ground truth dataset on artwork relation interestingness based on 7894 interestingness ratings from 320 participants across a selection of 136 artwork relations. 2. We present and evaluate various Wikidata-based artwork relation interestingness heuristics. 3. We show the extent to which there is a consensus on the types of artwork relations that art museum visitors consider (un)interesting. 4. We highlight several automatically identifiable artwork relation characteristics that help estimate the types of artwork relations art museum visitors consider to be interesting. 5. We confirm the considerable potential for improving the art museum visitor’s experience by explicitly identifying (interesting) artwork relations.