Empirical studies consistently report that labour productivity and TFP rise with city size. The reason is that cities attract the most productive agents, select the best of them, and make the selected ones even more productive via various agglomeration economies. This paper provides a microeconomically founded model of vertical city differentiation in which the latter two mechanisms (`agglomeration' and `selection') operate simultaneously. Our model is both rich and tractable enough to allow for a detailed investigation of when cities emerge, what determines their size, and how they interact through the channels of trade. We then uncover stylised facts and suggestive econometric evidence that are consistent with the most distinctive equilibrium features of our model. We show, in particular, that larger cities are both more productive and more unequal (`polarised'), that inter-city trade is associated with higher income inequalities, and that the proximity of large urban centres inhibits the development of nearby cities.