Abstract: I will report on a pair of studies that used fMRI responses to naturalistic story listening to shed light on critical debates in the study of human language processing: (1) whether typical language processing involves detailed word-by-word syntactic analysis or is largely approximate and shallow, (2) whether language processing demand is dominated by prediction or memory operations, and (3) whether domain-general cognitive control is involved in prediction or working memory for language. Our analyses used continuous-time deconvolution regression to estimate the hemodynamic response from data, with rigorous out-of-sample hypothesis tests. Findings converge to support (1) incremental construction of rich syntactic analyses, (2) dissociable effects of prediction and working memory demand, and (3) domain-specificity of prediction and working memory mechanisms for language, despite superficial similarity to prediction and working memory required by other cognitive domains. These results inform our understanding of the types of computations that are central to core language comprehension, as well as the domain-specificity of the neural resources that support those computations.