Highlights: What are the main findings? Morphing UAVs employ diverse mechanisms including closed-chain linkages, bioinspired structures, and compliant materials, enabling versatile geometric adaptability. Control strategies such as reinforcement learning, sliding mode control, and model predictive control improve stability during dynamic morphology changes. What is the implication of the main finding? Integration of morphing mechanisms with adaptive control expands UAV operational capabilities, supporting missions in confined spaces and critical applications like wildfire suppression. This review explores recent advancements in morphing structures for Unmanned Ariel Vehicles (UAVs), focusing on mechanical designs and control strategies of quadrotors that enable real-time geometric reconfiguration. Morphing mechanisms, ranging from closed-loop linkages to bioinspired and compliant structures, are evaluated in terms of adaptability, actuation simplicity, and flight stability. Control approaches, including model predictive control, reinforcement learning, and sliding mode control, are analyzed for their effectiveness in handling dynamic morphology. The review also highlights key morphing wing concepts such as GNATSpar and Zigzag Wingbox, which enhance aerodynamic efficiency and structural flexibility. A novel concept featuring an inverted slider-crank mechanism (ISCM) is introduced, enabling dual-mode UAV operation for both aerial and terrestrial missions, which is particularly useful in scenarios like wildfire suppression where stability and operation longevity are crucial. This study emphasizes the importance of integrated design approaches that align mechanical transformation with adaptive control. Critical gaps in real-world testing, swarm coordination, and scalable morphing architectures are identified, suggesting future research directions for developing robust, mission-adaptive UAV systems.