This paper presents a comprehensive review of nonlinear geometric control strategies for unmanned helicopters or aerial vehicles. Unlike traditional control methods relying on local linearization or minimal angle representations, geometric control is directly formulated on manifolds such as SE(3), ensuring global applicability without singularities. We review theoretical foundations, highlight major contributions in robust trajectory tracking, payload transport, and aggressive maneuver execution, and explore advanced integrations with deep learning and event-triggered frameworks. Applications in aerial load transportation, backflips, and resource-constrained operations are discussed. The review identifies key challenges, including computational complexity, real-time implementation, and integration with perception, and outlines promising future research directions in combining geometric control with AI-driven adaptation and autonomy.