The advancement of drone technology has underscored the critical need for adaptability and enhanced functionality in unmanned aerial vehicles (UAVs). Morphing quadrotors, capable of dynamically altering their structure during flight, offer a promising solution to extend and optimize the operational capabilities of conventional drones. This paper presents a comprehensive review of current advancements in morphing quadrotor research, focusing on morphing concept, actuation mechanisms and flight control strategies. We examine various active morphing approaches, including the integration of smart materials and advanced actuators that facilitate real-time structural adjustments to meet diverse mission requirements. Key design considerations—such as structural integrity, weight distribution, and control algorithms—are meticulously analyzed to assess their impact on the performance and reliability of morphing quadrotors. Despite their significant potential, morphing quadrotors face challenges related to increased design complexity, higher energy consumption, and the integration of sophisticated control systems. The discussion on challenges and opportunities highlights the necessity for ongoing advancements in morphing quadrotor technologies, particularly in addressing adaptive control problems associated with highly nonlinear and dynamic morphing aircraft systems, and in the potential integration with smart materials. By synthesizing the latest research and outlining prospective directions, this paper aims to serve as a valuable reference for researchers and practitioners dedicated to advancing the field of morphing quadrotor technologies.