Understanding the computations involved in language acquisition is a central topic in cognitive science. This dissertation presents four empirical papers that investigate the role of domain general cognitive processes in the learning of linguistic structure. The first paper describes the contribution of chunking—a basic memory process—to the phenomenon known as statistical learning, which describes learners’ ability to leverage the regularities present in the environment to form concrete representations of the input, such as finding the words in speech. The second paper extends these findings by showing how chunking can also account for the statistical learning and generalization of non-adjacent dependencies, a key feature of many linguistic systems. The third paper demonstrates that individual differences in statistically-based chunking of artificial language statistics significantly predicts sensitivity to comparable statistical structures in natural language. The final paper presents a meta-analysis of nearly 500 peer-reviewed studies on statistical learning in infants, children, and adults, tests its utility across different language properties, and proposes several methodological considerations that may benefit future experimentation. Together, these studies highlight the fundamental contribution of basic, domain general computations to language—and how they may even shape the evolution of linguistic structure over time.