Artificial intelligence (AI) has transformed various aspects of education, with large language models (LLMs) driving advancements in automated tutoring, assessment, and content generation. However, conventional LLMs are constrained by their reliance on static training data, limited adaptability, and lack of reasoning. To address these limitations and foster more sustainable technological practices, AI agents have emerged as a promising new avenue for educational innovation. In this review, we examine agentic workflows in education according to four major paradigms: reflection, planning, tool use, and multi-agent collaboration. We critically analyze the role of AI agents in education through these key design paradigms, exploring their advantages, applications, and challenges. To illustrate the practical potential of agentic systems, we present a proof-of-concept application: a multi-agent framework for automated essay scoring. Preliminary results suggest this agentic approach may offer improved consistency compared to stand-alone LLMs. Our findings highlight the transformative potential of AI agents in educational settings while underscoring the need for further research into their interpretability, trustworthiness, and sustainable impact on pedagogical impact.