© The Authors 2017. Published by Oxford University Press. This paper overviews the role of slums in urban Africa, focusing on Nairobi. It reveals the characteristics of slums and how these have changed over time. Spatially disaggregated data show that slum areas are very dense with poor-quality buildings, lacking access to key services such as sewage disposal and electricity. However, improvements to building quality, public-service provision, and socio-economic characteristics are mostly outpacing those seen in the formal sector. Measures such as child health and school attendance have caught up or are on pace to catch up in the near future with the formal sector, while improvements in building quality and service provision are advancing more slowly. We find significant heterogeneity across the city, and in particular that central slums look to be 'stuck' with low-quality buildings and poor service provision, though not with low socio-economic indicators. We explore potential explanations for why slums located on highly prized land near the centre may be stuck with poor infrastructure.