Open data can support the creation of new services, facilitate research, and provide insights into everyday issues affecting citizens. Although public administrations are making efforts to create sustainable and inclusive open data systems, there is limited capacity to identify suitable datasets, clean, release, and reuse them. Serious games offer a possible solution for data capacity building and have already been used to train civil servants and citizens on the topic of open data. This research presents a review of serious games and discusses their potential for data capacity building. The games selected in the review are classified and described according to their different learning outcomes, formats, and type of media. Most serious games found in this review can be categorized as teaching games and are designed to raise data awareness, which is only a limited aspect of building data capacity. We found a lack of design games, research games, and policy games. Given their success for ideation in other fields, design games offer a particular opportunity to build data capacity by generating new ideas about how to reuse open datasets.