Large language models (LLMs) have revolutionized artificial intelligence (AI) by enabling advanced natural language processing and generation capabilities. However, their widespread adoption brings significant challenges related to trustworthiness, responsibility, and ethical considerations. This chapter explores the critical issues surrounding the development and deployment of LLMs, focusing on bias, fairness, misinformation, privacy, and transparency. It highlights the importance of addressing these challenges to ensure that LLMs align with human-centered values and contribute positively to the society. The chapter reviews the architecture and evolution of LLMs, from early models like Generative Pre-trained Transformer (GPT) to advanced systems such as GPT-4, and examines their diverse applications. It also discusses frameworks and strategies for responsible AI development, including bias mitigation techniques, robustness, explainability, and human-in-the-loop approaches. Through case studies and real-world examples, the chapter illustrates both successes and failures in ensuring the trustworthiness of LLMs. Finally, it outlines future research directions and interdisciplinary approaches to advancing responsible AI. By providing a comprehensive roadmap, this chapter aims to guide researchers, developers, and policymakers in creating LLMs that are ethical, fair, and transparent, fostering public trust and ensuring their beneficial impact on the society.