The rapid advancements in Large Language Models (LLMs) have revolutionized natural language processing, enabling applications ranging from conversational agents to automated content generation. Despite their success, these models remain largely opaque, posing significant challenges to their explainability. This opacity stands in contrast to a core design principle in human-centered AI, which is “Transparency and Explainability,” that emphasizes on providing clear and understandable AI outputs to enhance user trust and empower informed decision-making. As a result, there is growing interest in developing techniques to make LLMs more transparent, particularly for high-stakes scenarios such as mortgage approvals or job interviews. This chapter explores current challenges, methods, and evaluation frameworks for LLM explainability. First, an overview on common definitions and terms associated with explainability for LLMs is presented. Second, a discussion on the challenges is presented, delving into the tension between human-understandable explanations and model-faithful representations, highlighting the difficulty of balancing simplicity and accuracy. Third, the chapter presents recent explainability methods for LLMs covering those adapted from the broader field of artificial intelligence explainability as well as methods developed specifically for LLMs. Then, key dimensions for evaluating explanations are examined, followed by a discussion on the current research questions in this area. The chapter concludes by addressing the most relevant challenges and future directions in explainability for LLMs. By providing an in-depth analysis of the state-of-the-art methods and existing challenges, this chapter aims to stimulate discussion on bridging the gap between technical innovations and their societal implications. It also highlights the need for interdisciplinary approaches to enhance the transparency and accountability of LLMs while maintaining their utility.