Technology has become an essential part of our everyday life, and its use in educational environments keeps growing. In addition, games are one of the most popular activities across cultures and ages, and there is ample evidence that supports the benefits of using games for assessment. This field is commonly known as game-based assessment (GBA), which refers to the use of games to assess learners' competencies, skills, or knowledge. In this article, we analyze the current status of the GBA field by performing the first systematic literature review on empirical GBA studies. It is based on 65 research papers that used digital GBAs to determine: the context where the study has been applied, the primary purpose, the domain of the game used, game/tool availability, the size of the data sample, the computational methods and algorithms applied, the targeted stakeholders of the study, and what limitations and challenges are reported by authors. Based on the categories established and our analysis, the findings suggest that GBAs are mainly used in K-16 education and for assessment purposes, and that most GBAs focus on assessing STEM content, and cognitive and soft skills. Furthermore, the current limitations indicate that future GBA research would benefit from the use of bigger data samples and more specialized algorithms. Based on our results, we discuss current trends in the field and open challenges (including replication and validation problems), providing recommendations for the future research agenda of the GBA field.