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Artificial intelligence (AI) in education (AIED) has evolved into a substantial body of literature with diverse perspectives. In this review paper, we seek insights into three critical questions: (1) What are the primary categories of AI applications explored in the education field? (2) What are the predominant research topics and their key findings? (3) What is the status of major research design elements, including guiding theories, methodologies, and research contexts? A bibliometric analysis of 2,223 research articles followed by a content analysis of selected 125 papers reveals a comprehensive conceptual structure of the existing literature. The extant AIED research spans a wide spectrum of applications, encompassing those for adaptive learning and personalized tutoring, intelligent assessment and management, profiling and prediction, and emerging products. Research topics delve into both the technical design of education systems and the examination of the adoption, impacts, and challenges associated with AIED. Furthermore, this review highlights the diverse range of theories applied in the AIED literature, the multidisciplinary nature of publication venues, and underexplored research areas. In sum, this research offers valuable insights for interested scholars to comprehend the current state of AIED research and identify future research opportunities in this dynamic field.