With the advancement of Artificial Intelligence (AI) and Large Language Models (LLMs), there is a profound transformation occurring in the realm of natural language processing tasks within the legal domain. The capabilities of LLMs are increasingly demonstrating unique roles in the legal sector, bringing both distinctive benefits and various challenges. This survey delves into the synergy between LLMs and the legal system, such as their applications in tasks like legal text comprehension, case retrieval, and analysis. Furthermore, this survey highlights key challenges faced by LLMs in the legal domain, including bias, interpretability, and ethical considerations, as well as how researchers are addressing these issues. The survey showcases the latest advancements in fine-tuned legal LLMs tailored for various legal systems, along with legal datasets available for fine-tuning LLMs in various languages. Additionally, it proposes directions for future research and development.