As the world increasingly urbanizes, the imaginaries, conceptions and politics of urban density will become increasingly urgent for research, policy, practice and activism. Density is a keyword in the history of how the city has been conceived and understood, and is firmly back on the global urban agenda. However, we lack sustained studies of how the geographies of density have been defined, lived, and contested. This paper develops a topological approach to urban density, considers key ways in which density has been politicized, and examines an emerging research area that understands the life and politics of density as ‘intensive heterogeneities’.