Now the city is considered as a phenomenon of the modern world. Cities develop according to their own laws and have a huge impact not only on the surrounding territories, but become centers of influence on global processes, acquiring or modernizing their old functions. The paper sets out ideas about the functions of cities, taking into account the specifics of their development. Changes in the functions of cities on the example of individual cities of Ukraine, France and Hungary are considered. The final part of the book outlines the main challenges of the modern urbanized world.