Smart city situational awareness has recently emerged as a hot topic in research societies, industries, and governments because of its potential to integrate cutting-edge information technology and solve urgent challenges that modern cities face. For example, in the latest five-year plan, the Chinese government has highlighted the demand to empower smart city management with new technologies such as big data and Internet of Things, for which situational awareness is normally the crucial first step. While traditional static surveillance data on cities have been available for decades, this review reports a type of relatively new yet highly important urban data source, i.e., the big mobile data collected by devices with various levels of mobility representing the movement and distribution of public and private agents in the city. We especially focus on smart city situational awareness enabled by synthesizing the localization of hundreds of thousands of mobile software Apps using the Global Positioning System (GPS). This technique enjoys advantages such as a large penetration rate (~50% urban population covered), uniform spatiotemporal coverage, and high localization precision. We first discuss the pragmatic requirements for smart city situational awareness and the challenges faced. Then we introduce two suites of empowering technologies that help fulfill the requirements of (1) cybersecurity insurance for smart cities and (2) spatiotemporal modeling and visualization for situational awareness, both via big mobile data. The main contributions of this review lie in the description of a comprehensive technological framework for smart city situational awareness and the demonstration of its feasibility via real-world applications.