With the rapid development of artificial intelligence technology, large language models (LLMs) have become a hot research topic. Education plays an important role in human social development and progress. Traditional education faces challenges such as individual student differences, insufficient allocation of teaching resources, and assessment of teaching effectiveness. Therefore, the applications of LLMs in the field of digital/smart education have broad prospects. The research on educational large models (EduLLMs) is constantly evolving, providing new methods and approaches to achieve personalized learning, intelligent tutoring, and educational assessment goals, thereby improving the quality of education and the learning experience. This article aims to investigate and summarize the application of LLMs in smart education. It first introduces the research background and motivation of LLMs and explains the essence of LLMs. It then discusses the relationship between digital education and EduLLMs and summarizes the current research status of educational large models. The main contributions are the systematic summary and vision of the research background, motivation, and application of large models for education (LLM4Edu). By reviewing existing research, this article provides guidance and insights for educators, researchers, and policy-makers to gain a deep understanding of the potential and challenges of LLM4Edu. It further provides guidance for further advancing the development and application of LLM4Edu, while still facing technical, ethical, and practical challenges requiring further research and exploration.