Artificial Intelligence increasingly pursues large, complex models that perform many tasks within increasingly realistic domains. How, if at all, should these developments in AI influence cognitive science? We argue that progress in AI offers timely opportunities for cognitive science to embrace experiments with increasingly naturalistic stimuli, tasks, and behaviors; and computational models that can accommodate these changes. We first review a growing body of research spanning neuroscience, cognitive science, and AI that suggests that incorporating a broader range of naturalistic experimental paradigms (and models that accommodate them) may be necessary to resolve some aspects of natural intelligence and ensure that our theories generalize. We then suggest that integrating recent progress in AI and cognitive science will enable us to engage with more naturalistic phenomena without giving up experimental control or the pursuit of theoretically grounded understanding. We offer practical guidance on how methodological practices can contribute to cumulative progress in naturalistic computational cognitive science, and illustrate a path towards building computational models that solve the real problems of natural cognition - together with a reductive understanding of the processes and principles by which they do so.