Unmanned Aerial Vehicles (UAVs) have emerged as a transformative technology across diverse sectors, offering adaptable solutions to complex challenges in both military and civilian domains. Their expanding capabilities present a platform for further advancement by integrating cutting-edge computational tools like Artificial Intelligence (AI) and Machine Learning (ML) algorithms. These advancements have significantly impacted various facets of human life, fostering an era of unparalleled efficiency and convenience. Large Language Models (LLMs), a key component of AI, exhibit remarkable learning and adaptation capabilities within deployed environments, demonstrating an evolving form of intelligence with the potential to approach human-level proficiency. This work explores the significant potential of integrating UAVs and LLMs to propel the development of autonomous systems. We comprehensively review LLM architectures, evaluating their suitability for UAV integration. Additionally, we summarize the state-of-the-art LLM-based UAV architectures and identify novel opportunities for LLM embedding within UAV frameworks. Notably, we focus on leveraging LLMs to refine data analysis and decision-making processes, specifically for enhanced spectral sensing and sharing in UAV applications. Furthermore, we investigate how LLM integration expands the scope of existing UAV applications, enabling autonomous data processing, improved decision-making, and faster response times in emergency scenarios like disaster response and network restoration. Finally, we highlight crucial areas for future research that are critical for facilitating the effective integration of LLMs and UAVs.