The concepts of Smart City and the Internet of Things have become a frequent topic of discussion in recent years. Due to the changes that take place in cities and the challenges cities face, modern solutions are sought to improve their functioning and enable their development. The aim of this paper was to demonstrate whether the Internet of Things is an essential element of a smart city. In the first part of the paper, the author focused on an introductory presentation of the basic problems of modern cities and defining the concept of Smart City. In the second part, the author focused on the Internet of Things and the description of selected technologies, with particular emphasis on their usefulness in the city. The last part of the paper showed how many elements of modern cities are closely related to the Internet of Things. The author presented real solutions implemented in smart cities, indicating that solutions based on the Internet of Things can be useful in every area of a smart city.