In the last ten years, new sources of urban big data have made it possible for algorithms to increasingly control how the city is perceived, understood and managed by its inhabitants; this is the data-driven city. New efforts in the social sciences, like critical data studies, are beginning to describe the ways in which urban data is never completely objective and how its logics influence and shape our everyday physical world. In this thesis I transfer insights from critical data studies to architecture, asking how the emergence of data-driven urbanism is influencing architecture as practice and artifact and, conversely, what impact architecture can make in an urban context dominated by big data. To answer these questions I take on three place-based case studies which highlight controversial urban problems managed by automated practices of measuring, mapping and procedural response: aviation noise near Heathrow Airport, storm floods in Amsterdam and population density in Singapore. Though data-driven, these cases nonetheless demonstrate the persistent importance of the design of the built environment to the function of these urban systems. To make a comparative analysis of the three case studies and to provide a framework to interrogate the impact of architectural interventions, I introduce a new conceptual tool: the data-genealogy tree. I use the data-genealogy tree to (1) chart how metrics, institutions, architectural elements and software are brought into a data-mediated socio-technical system, (2) to assess over time the growing embeddedness of this socio-technical system in each case study, and (3) to identify reorientation points when motivations of the socio-technical system have changed and innovations emerged. Examining the association of architectural artifacts with the reorientation points charted in the data-genealogy tree makes possible an assessment of the impact of architectural interventions and provides a basis for describing more generally how the architect may seek to influence the development of the data-driven city. As an ensemble, the architectural interventions described in the case studies also provide evidence for a description of the formal evolution of architecture in the data-driven city. The case studies suggest that singular architectural artifacts are less relevant to this context than catalogues of architectural elements which are made open to quantification and tracking and can assemble into many possible configurations in response to the demands of urban systems. Finally, I consider how design process is changing in the data-driven city, describing how architects in the case studies have worked with urban data to cross disciplinary silos or recruit wider stakeholder participation in consensus design solutions.