Large Language Model (LLM) agents have demonstrated remarkable capabilities in automating tasks and driving innovation across diverse educational applications. In this survey, we provide a systematic review of state-of-the-art research on LLM agents in education, categorizing them into two broad classes: (1) \emph{Pedagogical Agents}, which focus on automating complex pedagogical tasks to support both teachers and students; and (2) \emph{Domain-Specific Educational Agents}, which are tailored for specialized fields such as science education, language learning, and professional development. We comprehensively examine the technological advancements underlying these LLM agents, including key datasets, benchmarks, and algorithmic frameworks that drive their effectiveness. Furthermore, we discuss critical challenges such as privacy, bias and fairness concerns, hallucination mitigation, and integration with existing educational ecosystems. This survey aims to provide a comprehensive technological overview of LLM agents for education, fostering further research and collaboration to enhance their impact for the greater good of learners and educators alike.