Generative artificial intelligence (GAI) has demonstrated remarkable potential in both educational practice and research, particularly in areas, such as personalized learning, adaptive assessment, innovative teaching methods, and cross-cultural communication. However, it faces several significant challenges, including the comprehension of complex domain knowledge, technological accessibility, and the delineation of AI's role in education. Addressing these challenges necessitates collaborative efforts from educators and researchers. This article summarizes the state-of-the-art large language models (LLMs) developed by various technology companies, exploring their diverse applications and unique contributions to primary, higher, and vocational education. Furthermore, it reviews recent research from the past three years, focusing on the challenges and solutions associated with GAI in educational practice and research. The aim of the review is to provide novel insights for enhancing human-computer interaction in educational settings through the utilization of GAI. Statistical analysis reveals that the current application of LLMs in the education sector is predominantly centered on the ChatGPT series. A key focus for future research lies in effectively integrating a broader range of LLMs into educational tasks, with particular emphasis on the interaction between multimodal LLMs and educational scenarios.