Platform urbanism has emerged in recent years as an area of research into the ways in which digital platforms are increasingly central to the governance, economy, experience, and understanding of the city. In the paper, we argue that platform urbanism is an evolution of the smart city, constituted by novel, digitally-enabled socio-technical assemblages that enable new forms of social, economic and political intermediation. We offer a typological framework for a better conceptualization of platform urbanism and its complex socio-economic relationships. We further outline several directions for future research on platform urbanism, specifically: a.) the need to critically investigate new power geometries of corporate, legal and regulatory alignments; b.) how platform urbanism may be expressed in, and affect, cities in the Global South; c.) how it may need to be critically engaged with in regard to its development in response to emergent events such as the Covid-19 pandemic; and d.) how it may shape visions of the current and future city.