How can people live together, with ever more diverse characteristics, in the world’s rapidly expanding cities? Current global migration flows show profound diversification of migrants’ nationalities, ethnicities, languages, gender balances, age profiles, human capital and legal statuses. Across the globe, such processes have created conditions of urban ‘super-diversity’. Everywhere, recent migrants with complex ‘new diversity’ traits now dwell in cities alongside people from previous, ‘old diversity’ waves, often within long-established ethnic/racial hierarchies. What will social relations, spatial patterns, political mobilizations and structures of inequality look like in tomorrow’s ever more complex urban spaces?