This structured integrative review surveys Intelligent Systems in Education through a function-first taxonomy that groups systems by pedagogical role rather than algorithm. It synthesizes eight families—adaptive tutoring, assessment and feedback, student modeling, analytics, collaboration support, content generation, game-based learning, and cross-function integration—and traces how data moves among them. Across families, the field is shifting from stand-alone tools toward interoperable ecosystems. The review highlights recurring challenges in long-term adaptivity, generative reliability, fairness and privacy, teacher–artificial intelligence (AI) collaboration, and system-level evaluation.