Digital innovations in insurance, ‘InsurTech’, bring together two transformational forces in our contemporary world – risk and digitization. InsurTech has been celebrated and criticized. A literature on the social studies of insurance provides valuable and more nuanced insights into the social, cultural, and technological properties of InsurTech but it tends to analyze these at the firm level. This article brings together themes from assemblage and international political economy theories to integrate analysis of the structure of the global industry and the role of cross-border regulatory arrangements with the firm-level insights of the social studies of insurance literature. The article examines differentiation in the industry structure between stages of the insurance value chain, between incumbent and start-up insurers and Big Tech, and across jurisdictions and regions. It also examines the most globally significant regulatory responses to InsurTech: from the International Association of Insurance Supervisors, the European Insurance and Occupational Pensions Authority, the China Banking and Insurance Regulatory Commission, and the US National Association of Insurance Commissioners. It shows that the nuance and ethical content that is evident at the firm level in the social studies of insurance literature is interacting with similar nuance and ethical content in global regulatory arrangements.