The pervasive integration of Unmanned Aerial Vehicles (UAVs) across multifarious domains necessitates a nuanced understanding of control methodologies to ensure their optimal functionality. This exhaustive review meticulously examines two pivotal control paradigms in the UAV landscape, Geometric Control and Feedback Linearization. Delving into the intricate theoretical underpinnings, practical applications, strengths, and challenges of these methodologies, the paper endeavors to provide a comprehensive overview. Geometric Control, grounded in the principles of differential geometry, offers an elegant and intuitive approach to trajectory tracking and mission execution. In contrast, Feedback Linearization employs nonlinear control techniques to linearize UAV dynamics, paving the way for enhanced controllability. This review not only dissects the theoretical foundations but also scrutinizes real-world applications, integration challenges, and the ongoing research trajectory of Geometric Control and Feedback Linearization in the realm of UAVs.