Recent technological developments and the availability of enormous amounts of real-time data have played a vital role in the expansion, evolution, and success of smart city projects. Smart data can be used in a variety of smart city applications, but difficulties in managing such data are pushing smart cities toward the adoption of data management frameworks. Many studies have brought into focus the importance of these frameworks as they combine data collection, processing, analysis, management, and visualization and provide privacy and security features for different smart city applications, i.e., transportation, to promote a better quality of life. This chapter highlights key components of the data management framework, reviews various smart city applications, and discusses privacy and security challenges associated with smart city data. From the perspective of data frameworks, it is seen that the data used in smart city applications is unstructured coming from heterogeneous sources, i.e., sensors and social media, besides others. Therefore, the collection, processing, analysis, management, and visualization of such data are challenging. To perform these tasks, recent technologies, i.e., Internet of Things (IoT), sensor networks, machine learning, etc., have been used. Moreover, the use of smart data for smart government and governance provides several facilities for the public and business. The smart data is revolutionizing the daily communication of users along with their mode of transportation by introducing Social IoT (SIoT) and autonomous vehicles. Lastly, the challenges related to privacy and security of the data in smart cities that needed to be addressed are highlighted. This chapter will guide academics and enterprises to progress in data management framework and its applications in smart cities in the near future.