With the development of the Large Language Models (LLMs), a large range of LLM-based Text-to-SQL(Text2SQL) methods have emerged. This survey provides a comprehensive review of LLM-based Text2SQL studies. We first enumerate classic benchmarks and evaluation metrics. For the two mainstream methods, prompt engineering and finetuning, we introduce a comprehensive taxonomy and offer practical insights into each subcategory. We present an overall analysis of the above methods and various models evaluated on well-known datasets and extract some characteristics. Finally, we discuss the challenges and future directions in this field.