The current era of global urbanization is defined by a convergence of economic and political crises requiring urgent sociological reflection on the meaning of the ‘urban' today. This article responds to the current rethinking of worldwide processes of urbanization sparked off by Brenner, and Brenner and Schmid, arguing for a renewed sociological approach to urban formations that probes beyond the economic logic of urban ‘de‐territorialization', towards the capricious life‐worlds and forms of planetary organization that define the urban. We pursue a theory of the ‘urban vortex' to capture the maelstrom of disorienting crises since 2008, and explicate the social formations implicated in the construction, materialization and practice of power and transgression in cities today. Our aim is to consider what forms of social change emerge in volatile, intense and centralized dynamics (the urban vortex), and how this might relate to arrangements of interconnectivity, particularity and variegation (the planetary). The article highlights three prominent processes of urban social formation: accumulation, stratification and hyper‐diversity—reinstating the need to theorize the centrality of the city within the formations of twenty‐first century capitalism.