Digital platforms have become integral to contemporary schooling. Google Classroom, Compass, Office 365, EdQuire, ClassDojo and Canvas are just some of the many platforms that litter students' and teachers' computers today. While students may have only one school to physically attend, there is a labyrinth of digital enclosures for them to navigate as part of their schooling. The rise of digital platforms in education has occurred at an erratic rate--sometimes through function creep, sometimes through whole system mandates, and certainly the global pandemic has accelerated their rise. In this article we consider how platforms have become an infrastructure in education and the implications this has for teaching, learning and the relationships between key stakeholders. We provide an overview of the education research into platforms to date, highlighting areas that require further empirical and theoretical investigation. We conclude the article by outlining a research agenda for critical platform studies in education.