Science, already a massive and global enterprise, continues to grow in both size and complexity. Accompanying this growth is a deluge of data on scientific activity and advancements in computational techniques that open new avenues for its analysis. Leveraging these new data and techniques, the field of Science of Science turns the tools of science upon science itself, aiming to understand its composition and behavior. While making significant contributions, the study of science remains constrained by its vastness, heterogeneity, and interconnectedness. Here, I argue that the Science of Science benefits from viewing science as a complex system, and drawing on the conceptual framework developed to understand such systems in other domains. Specifically, I detail a complexity perspective that conceptualizes science as a self-organizing system of interconnected scientists in which bottom-up interactions between individuals give way to emergent global structure and behavior. I demonstrate the value of this perspective by using it to interpret four studies covering diverse topics in Science of Science: bias in peer review, prejudice in teaching evaluations of university faculty, the incidence of disagreement in science, and the landscape of global scientifc mobility. Viewing my findings through the lens of complexity, I disentangle the forces that contribute to the behavior of individual scientists and illustrate how feedback mechanisms simultaneously entrench social structures while maintaining the potential for revolutionary change. This perspective also reveals how the inherent complexity of science poses challenges for its study, confounding attempts at objective measurement. Finally, I argue that the complexity perspective is uniquely positioned to benefit from future advancements in data availability and methodology and to provide further insights into the fundamental composition and behaviors of science. Embracing complexity others a promising direction for the Science of Science, with deep implications for the understanding and governance of the global scientific enterprise.