Drones, or unmanned aerial vehicles (UAVs), are among the most beneficial and emerging technologies, with a wide range of applications that can support the sustainability concerns of smart cities and ultimately improve citizens’ quality of life. The goals of this systematic review were to explore the involvement of surveillance drones in smart cities in terms of application status, application areas, proposed models, and characteristics of drones. We conducted this systematic review based on the preferred reporting items for systematic reviews and meta-analyzes (PRISMA) guidelines. We systematically searched the Web of Science and Scopus for journal articles and conference papers written in English and published up to August 2021. Of the 323 records identified, 43 met the inclusion criteria. Findings showed that surveillance drones were used in seven distinct research fields (transportation, environment, infrastructure, object or people detection, disaster management, data collection, and other applications). Air pollution and traffic monitoring were the dominant application areas. The majority of reviewed models were based on the application of rotary-wing single-drones with the camera as the aerial sensor. Reviewed models showed that the adoption of a single or multiple UAVs, either as a stand-alone technology or integrated with other technologies (e.g., internet of things, wireless sensor networks, convolutional neural networks, artificial intelligence, machine learning, computer vision, cloud computing, web applications), can offer efficient and sustainable solutions compared to conventional surveillance methods. This review can benefit academic researchers and practitioners.