Unmanned Aerial Vehicles (UAVs) are pivotal in various applications, yet their widespread use exposes them to significant cybersecurity threats, including cyber, physical, and hybrid attacks. This paper presents a comprehensive review of current research and advancements in UAV cybersecurity. Key vulnerabilities such as GPS spoofing, jamming, malware, and physical attacks are discussed, highlighting their potential impact on UAV operations and data security. The review identifies innovative defense strategies and frameworks proposed to mitigate these threats, including advanced penetration testing techniques, dynamic defense frameworks, and algorithms like Stackelberg games and swarm intelligence. Addressing specific research questions, the paper explores recent advancements in the use of advanced penetration testing techniques to enhance UAV security, evaluates the effectiveness of penetration testing methodologies across different UAV components, and analyzes challenges associated with conducting such tests and potential mitigation strategies. Furthermore, the paper discusses future directions in UAV cybersecurity, emphasizing the integration of emerging technologies such as quantum computing resilience, adaptive defense mechanisms, and secure software-defined networking (SDN). These advancements aim to bolster UAV defenses, ensuring robust protection against current and future cybersecurity challenges in dynamic and hostile operational environments.