As a typical cyber-physical system, networked unmanned aerial vehicles (UAVs) have received much attention in recent years. Emerging communication technologies and high-performance control methods enable networked UAVs to operate as aerial sensor networks to collect more complete and consistent information with significantly improved mobility and flexibility than traditional sensing platforms. One of the main applications of networked UAVs is surveillance and monitoring, which constitute essential components of a well-functioning public safety system and many industrial applications. Although the existing literature on surveillance and monitoring UAVs is extensive, a comprehensive survey on this topic is lacking. This article classifies publications on networked UAVs for surveillance and monitoring using the targets of interest and analyzes several typical problems on this topic, including the control, navigation, and deployment optimization of UAVs. The related research gaps and future directions are also presented.