Our everyday life is entangled with products and services of so-called Big Tech companies, such as Amazon, Google, and Facebook. International relations (IR) scholars increasingly seek to reflect on the relationships between Big Tech, capitalism, and institutionalized politics, and they engage with the practices of algorithmic governance and platformization that shape and are shaped by Big Tech. This collective discussion advances these emerging debates by approaching Big Tech transversally, meaning that we problematize Big Tech as an object of study and raise a range of fundamental questions about its politics. The contributions demonstrate how a transversal perspective that cuts across sociomaterial, institutional, and disciplinary boundaries and framings opens up the study of the politics of Big Tech. The discussion brings to the fore perspectives on the ontologies of Big Tech, the politics of the aesthetics and credibility of Big Tech and rethinks the concepts of legitimacy and responsibility. The article thereby provides several inroads for how IR and international political sociology can leverage their analytical engagement with Big Tech and nurture imaginaries of alternative and subversive technopolitical futures.