Efforts to understand the brain bases of language face the mapping problem: at what level do linguistic computations and representations connect to human neurobiology? We review one approach to this problem that relies on rigorously defined computational models to specify the links between linguistic features and neural signals. Such tools can be used to estimate linguistic predictions, model linguistic features, or specify a sequence of processing steps that may be quantitatively fit to neural signals collected while participants use language. Progress has been helped by advances in machine learning, attention to linguistically interpretable models, and openly shared datasets that allow researchers to compare and contrast a variety of models. We describe one such dataset in detail in the supplementary materials.