In recent years, Amazon, Microsoft, and Google have become three of the dominant developers of AI infrastructures and services. The increasing economic and political power of these companies over the data, computing infrastructures, and AI expertise that play a central role in the development of contemporary AI technologies has led to major concerns among academic researchers, critical commentators, and policymakers addressing their market and monopoly power. Picking up on such macro-level political-economic analyses, this paper more specifically investigates the micro-material ways infrastructural power in AI is operated through the respective cloud AI infrastructures and services developed by their cloud platforms: AWS, Microsoft Azure, and Google Cloud. Through an empirical analysis of their evolutionary trajectories in the context of AI between January 2017 and April 2021, this paper argues that these cloud platforms attempt to exercise infrastructural power in three significant ways: through vertical integration, their complementary innovation, and the power of abstraction. Each dynamic is strategically mobilised to strengthen these platforms’ dominant position at the forefront of AI development and implementation. This complicates the critical evaluation and regulation of AI technologies by public authorities. At the same time, these forms of infrastructural power in the cloud provide Amazon, Microsoft, and Google with leverage to set the conditions of possibility for future AI production and deployment.