It is widely recognized that global urbanization is one the most urgent issue of our time. Any problem related to global issues, such as climate change, social and environmental sustainability and the future of our society, is somehow related to cities and urbanization. However, despite its great importance, general knowledge on cities still lacks a scientific and shared understanding. Traditional approach for understanding cities, mostly derived from urban planning practices and classical geography, have been proved to be unsuited to catch the great complexity of cities. In order to fill this gap, and thanks to the increasing amount of digital data, a new science of cities is arising. Embedded in physic and chemistry approaches, the new science of cities aims to provide quantitative and reproducible knowledge on urban form and dynamics. From urban scaling to complex networks, scientific approach to cities was able to provide evidence of the very top-down nature of urbanization and of the existence of some physical laws that govern urbanization beyond local conditions. The thesis, acknowledging the weak points of traditional approaches to cities, aims to provide a series of quantitative studies on urbanization patterns and urban dynamics. Six case studies explore several open questions providing new insights on the physical nature of urbanization process.