This paper offers an analysis of scientific creativity based on theoretical models and experimental results of the cognitive sciences. Its core idea is that scientific creativity--like other forms of creativity--is structured and constrained by prior ontological expectations. Analogies provide scientists with a powerful epistemic tool to overcome these constraints. While current research on analogies in scientific understanding focuses on near analogies, where target and source domain are close, we argue that distant analogies--where target and source domain differ widely--are especially useful in periods of intense conceptual change. To argue this point, we discuss three case studies from the history of science: early physiologists like Harvey, early evolutionary biologists like Darwin, and recent theorists on the evolution of the human mind like Mithen.