The dual urban-rural and center-periphery models have served as keys to describe and explain the function, structure and evolution of urban areas for geographers and more generally for social scientists. During the 20th century, many cities had seen their spatial extent and population doubling several times, their centers and their peripheries split, so that observers have stepped up efforts to acquire new words to account for changes in the city and its doubles. This article highlights their creativity, driven by the emergence of a model of the third kind, eminently urban, which corresponds to both the city and the countryside.