Massive increase in population of the cities has led to various problems, ranging from traffic jams, noise problems, environmental pollution, and many others. To prevent this, the concept of smart cities was developed. Today's smart cities are based on information and communication technology and Internet of Things technology. With these technologies, the devices connect to the Internet, and they have built-in sensors, meters and other elements important for the development of smart cities. The paper presents and describes a smart city, its architecture and factors, and deals in more detail with the topic of smart mobility of a smart city. The elements of smart transport, the stages of establishing smart transport and the ways of its use are presented. The connection between smart vehicles and shortcomings thereof are discussed as well as the shortcomings and problems of smart transport, proposing the solutions are that would improve transport in smart cities. The paper analyses the cases of two cities in Europe - Stockholm, which was declared the smartest city in Europe in 2020, and Zagreb. It also analyzes the impact of the pandemic on transport in smart cities, which for example resulted in large financial losses in the public transport sector due to the inability to operate it and also due to social distance requirement in public transport vehicles. At the same time, reduced traffic had a positive impact on the environment owing to reduced pollution. The digitization as well as innovative ideas and technology greatly contribute to solving these problems. In the methodical part, the preparation for teaching on the topic related to this thesis in high school is presented.