In recent years, the interest in the use of serious games as teaching and learning tools in traditional educational processes has increased significantly. Serious Educational Games (SEG) and Learning Analytics (LA) are gaining increasing attention from teachers and researchers, since they both can improve the learning quality. In this article, we aimed to examine, summarize and characterize the current state of the art related to the application of LA to SEGs through a systematic literature review based on a methodological instrument called PRISMA. A qualitative analysis was performed in which 80 significant papers were selected from the ScienceDirect, SpringerLink, Web of Science, and IEEE-Xplore databases. From this analysis, we identified the main features of an efficient use of SEGs in terms of success factors and learning outcomes; we also discussed the benefits and challenges of integrating LA approaches into these environments. Consequently, a new multidimensional taxonomy for using SEGs to categorize these major features was proposed. The findings of this review reveal that SEGs have a beneficial effect on students' behavior, cognition and emotion; but more future works and empirical studies investigating data science techniques are needed to improve the usability of educational games. This research and the suggested guideline recommendations may be of value to researchers and practitioners willing to deploy SEGs contributing thus to the continuous improvement of digital learning in formal education.