This study reviews 71 high-quality studies of massive open online courses focused on languages (LMOOCs) that were published from the inception of LMOOCs to 2021. The purpose of this study is to gain a deeper understanding of the current state of research and identify fruitful directions for future LMOOC research. First, we reviewed three basic sets of characteristics of these studies: (1) research trends -- for example, publication types and years; (2) research contexts -- for example, countries in which the studies were conducted, the subjects' target languages, language-ability levels, skills, and whether the focal courses are for specific purposes; and (3) research design, including data collection, data analysis, and theoretical frameworks. We then utilized a text-mining approach called Latent Dirichlet Allocation that uses machine-learning techniques to identify research-topic commonalities underlying the collected studies. In this way, a total of nine topics were identified. They were: (1) core elements of LMOOCs; (2) interaction and communication in LMOOCs; (3) innovative LMOOC teaching practices; (4) LMOOC standards and quality assurance; (5) LMOOC implementation, participation, and completion; (6) LMOOC teaching plans; (7) LMOOC learning effectiveness and its drivers/obstacles; (8) learners and learning in LMOOCs; and (9) inclusiveness in LMOOCs. These were then diagrammed as a ThemeRiver, which showed the evolutionary trend of the nine identified topics. Specifically, scholarly interest in Topics 5, 7, and 9 increased over time, whereas for Topics 1 and 6, it decreased. Based on our results, we highlighted specific directions for future LMOOC research on each of the identified research topics.