We construct a simple model of a city with heterogeneous agents and housing choice to explain the determinants of slums, home to about one-third of the urban population in developing countries. The model supports the main empirical evidence regarding slum formation and is able quantitatively to assess the role of each determinant of slum growth. We show that urban poverty, inequality and rural–urban migration explain much of the variation in slum growth in Brazil from 1980 to 2000. Ex ante evaluation of the impacts of policy interventions shows that removing barriers to formalisation has a strong impact on slum reduction.