A basic challenge for research into the neurobiology of language is understanding how the brain combines words to make complex representations. Linguistic theory divides this task into several computations including syntactic structure building and semantic composition. The close relationship between these computations, however, poses a strong challenge for efforts to distinguish them at the neural level. This dissertation develops and tests a hypothesis derived from the computational linguistics literature that these computations may dissociate when considered as incrementally applied operations. Under this approach, different theories of the relationship between syntactic and semantic computations carry distinct predictions about incremental processing load. In this dissertation, predictions from formal, psychologically grounded, models of incremental parsing are tested against brain data from two experiments using functional magnetic resonance imaging (fMRI) and magnetoencephalography (MEG). Results from these experiments, where participants perform relatively natural tasks (reading or listening to a story), provide novel evidence concerning the localization and timing of brain activity involved in building complex linguistic representations. Comparing brain activity with predictions from models based on two different grammatical architectures offers evidence favoring grammatical theories which distinguish structure building and semantic composition as separate types of computations. As such, this work contributes to a broader goal to develop new methods for using brain data to evaluate theoretically informed models of linguistic competence and performance.