With the increasing use of Artificial Intelligence (AI) technologies in education, the number of published studies in the field has increased. However, no large-scale reviews have been conducted to comprehensively investigate the various aspects of this field. Based on 4,519 publications from 2000 to 2019, we attempt to fill this gap and identify trends and topics related to AI applications in education (AIEd) using topic-based bibliometrics. Results of the review reveal an increasing interest in using AI for educational purposes from the academic community. The main research topics include intelligent tutoring systems for special education; natural language processing for language education; educational robots for AI education; educational data mining for performance prediction; discourse analysis in computer-supported collaborative learning; neural networks for teaching evaluation; affective computing for learner emotion detection; and recommender systems for personalized learning. We also discuss the challenges and future directions of AIEd.