Large Language Models (LLMs) have revolutionized natural language processing tasks, showcasing impressive abilities across various domains. This thesis explores their application within the insurance sector, focusing on tasks like classification and information extraction. The research centers on developing a system named InsureAI, which utilizes LLMs to automatically categorize insurance complaints across multiple levels and extract pertinent information from these complaints. The goal is to investigate the effectiveness of two different models - Llama-70b and Zephyr-7b - by employing two different approaches for implementing this system: zero-shot learning and instruction fine-tuning. The former uses the pre-trained knowledge of the model to perform inference while the latter further trains the LLM explicitly on a custom dataset of insurance complaints tailoring the model to the domain-specific dataset.