The Internet and Internet of Things (IoT) make the Smart City concept an achievable and attractive proposition. Efficient information abstraction and quick decision making, the most essential parts of situational awareness (SAW), are still complex due to the overwhelming amount of dynamic data and the tight constraints on processing time. In many urban surveillance tasks, powerful Cloud technology cannot satisfy the tight latency tolerance as the servers are allocated far from the sensing platform; in other words there is no guaranteed connection in the emergency situations. Therefore, data processing, information fusion and decision making are required to be executed on-site (i.e., near the data collection locations). Fog Computing, a recently proposed extension of Cloud Computing, enables on-site computing without migrating jobs to a remote Cloud. In this chapter, we firstly introduce the motivations and definition of smart cities as well as the existing challenges. Then the concepts and advantages of Fog Computing are discussed. Additionally, we investigate the feasibility of Fog Computing for real-time urban surveillance using speeding traffic detection as a case study. Adopting a drone to monitor the moving vehicles, a Fog Computing prototype is developed. The results validate the effectiveness of our Fog Computing based approach for on-site, online, uninterrupted urban surveillance tasks.