Abstract Complexity science permeates the policy spectrum but not antitrust. This is unfortunate. Complexity science provides a high-resolution screen on the empirical realities of markets. And it enables a rich understanding of competition, beyond the reductionist descriptions of markets and firms proposed by neoclassical models and their contemporary neo-Brandeisian critique. New insights arise from the key teachings of complexity science, like feedback loops and the role of uncertainty. The present article lays down the building blocks of a complexity-minded antitrust method.