On a sustained basis, cities are of non-uniform relative sizes. This paper addresses three basic issues which arise from this simple observation by examining the size distribution of US cities over the period 1900–1990. First, we explore the reasons why there is a wide distribution of city sizes. Second, we characterize the evolution of the size distribution of cities, documenting growth in sizes and numbers of cities. We ask whether the relative size distribution of cities has remained stable over time, or if it has displayed, instead, a tendency to collapse, flatten, or otherwise change its shape. We also examine evidence on whether the size distribution obeys Zipf's Law. Third, we examine the degree and determinants of mobility of individual cities within this distribution, asking to what extent cities are moving up and down in the distribution and how this movement is influenced by cities' geographic characteristics. We use a newly constructed data with consistent metropolitan area definitions over this century, discussing the issues and linking our results to the relevant literature.