The concept “Smart City” is realized by incorporating advanced sensing and computational technologies in various processes, services, and infrastructure. Internet of Things (IoT) and Cyber-Physical Systems (CPS) are the key role players in the major development of smart city infrastructure. Further, the CPS stationing has improved the quality of various services like healthcare, transportation, environmental, etc., provided in a typical smart city ecosystem. But, the embodiment of CPS has also increased the surface area for cyber-attacks. In this paper, the various security and privacy issues at the different levels in the architecture of a smart city are discussed. The domain-centric security issues evolved with the deployment of CPS in transportation, healthcare, smart grids, and smart homes are also explored. Scopus publications for the years 2016–2020 are considered for the bibliometric analysis in security. It has been observed that a major number of security solutions have been proposed in the domain of smart homes during these years, whereas much scope is still there to address security and privacy challenges for CPS equipped smart grids. But over time, the security of smart grids is also becoming an area of interest for researchers. The article is concluded with the research gaps and future scope to cater secure smart city services.