This review paper provides insights into optimization strategies for Unmanned Aerial Vehicles (UAVs) in a variety of surveillance tasks and scenarios. From basic path planning to complex mission execution, we comprehensively evaluate the multifaceted role of UAVs in critical areas such as infrastructure inspection, security surveillance, environmental monitoring, archaeological research, mining applications, etc. The paper analyzes in detail the effectiveness of UAVs in specific tasks, including power line and bridge inspections, search and rescue operations, police activities, and environmental monitoring. The focus is on the integration of advanced navigation algorithms and artificial intelligence technologies with UAV surveillance and the challenges of operating in complex environments. Looking ahead, this paper predicts trends in cooperative UAV surveillance networks and explores the potential of UAVs in more challenging scenarios. This review not only provides researchers with a comprehensive analysis of the current state of the art, but also highlights future research directions, aiming to engage and inspire readers to further explore the potential of UAVs in surveillance missions.