Large Language Models have quickly become the cornerstone of modern Artificial Intelligence, showcasing exceptional performance across a wide variety of natural language understanding and generation tasks. These models that are built on architectures, such as Transformers or Retrieval Augmented Generation (RAG's) to name a few and are trained on massive datasets have shown promising capabilities such as in-context learning, reasoning, and instruction following. In this chapter, a comprehensive explorative study is performed on the foundational principles underlying the workings of modern day LLMs including their architectures, training methodologies, and fine-tuning optimization techniques. Furthermore, this chapter delves deeper into the diverse applications across industries while also exploring the key technical challenges like hallucinations, biases, fairness, and scalability. Further research directions include advancements in efficiency, alignment with human preferences, and integration of external knowledge.