The integration of natural language processing techniques (NLP) into the legal domain has opened up new possibilities for automating, analyzing, and improving access to legal information. However, the complex and specialized terminology of legal texts has always been a significant challenge for the NLP area. To overcome this challenge, research studies in the law domain conducted with NLP techniques can be categorized into the following tasks: classification, information extraction, summarization, information retrieval, legal judgment prediction. Recent advancements in large language models (LLMs) have significantly contributed to NLP tasks across various domains, including the aforementioned tasks in the legal domain. The ability of large language models to reason and understand the deep context of texts has shown promising capabilities for understanding legal language and overcoming legal challenges. Therefore, this paper explores the existing tasks addressed by NLP in the legal domain and delves into LLM-based approaches which address these NLP tasks. Moreover, the datasets and evaluation criteria for LLMs have been examined, and the challenges and key limitations of LLMs in the legal domain have been identified. Hallucination, lack of domain-specific knowledge, and lack of interpretability have been determined as the challenges for the reliable application of large language models in the legal field. Finally, opportunities for future research have been discussed.