The recent years have seen the rise of the so-called replication crisis in psychology, and, by association, cognitive science. Two broad camps have been formed around the appropriate way to combat this crisis: one that blames sloppiness in data collection, and a smaller one that blames weak or vague theoretical commitments. In this dissertation, I argue that some dimensions of these issues belong in the mediating level of models, the bridges that interface with theory and data. The three studies contained in the dissertation attempt to illustrate the knowledge-creation potential of modeling work using computational tools. Chapter 2 applies this approach to the phenomenon of sound systematicity, patterns of similarity that link sound and meaning in language. By modeling a typologically diverse data set, we find evidence that sound systematicity is a widespread phenomenon in the world’s languages. Chapter 3 evaluates the grasp of advanced language use of a large language model, GPT-3, through the generation of poetry. We found that its performance at this task is on par, if not superior to, naïve human participants given the same task. This has the potential to refute the long-standing assumption that acquiring adult-like language from experience is impossible. Finally, Chapter 4 showcases the potential of computational modeling to engage with foundational theoretical issues by exploring a model of interdisciplinary work as a mixture of expertise. We apply it to a recent debate about cognitive science’s supposed collapse into psychology but find no evidence that the former is becoming less interdisciplinary. Instead, we advance and assess the hypothesis that the perception of stagnation stems from a weakened theoretical consensus in the field. Overall, the studies contained here suggest that models, by engaging with both theory and data while not being determined by either of them, can be a source of genuine knowledge. Among other functions, I hope to show that computational bridges can expand the range of data available for theorizing; provide a common space for exploring the consequences of both observations and assumptions; and strengthen our grasp of the phenomena that we posit underlie our interactions with nature.