The rapid advancement of Transformer-based models has reshaped the landscape of uncrewed aerial vehicle (UAV) systems by enhancing perception, decision-making, and autonomy. This review paper systematically categorizes and evaluates recent developments in Transformer architectures applied to UAVs, including attention mechanisms, CNN-Transformer hybrids, reinforcement learning Transformers, and large language models (LLMs). Unlike previous surveys, this work presents a unified taxonomy of Transformer-based UAV models, highlights emerging applications such as precision agriculture and autonomous navigation, and provides comparative analyses through structured tables and performance benchmarks. The paper also reviews key datasets, simulators, and evaluation metrics used in the field. Furthermore, it identifies existing gaps in the literature, outlines critical challenges in computational efficiency and real-time deployment, and offers future research directions. This comprehensive synthesis aims to guide researchers and practitioners in understanding and advancing Transformer-driven UAV technologies.