Syntactic structures relate the meanings of the individual words in sentences to one another, thus allowing sentences to express propositions that can be entered into memory, used in reasoning and planning, and serve as the basis for much of human thought and expression. Syntactic structures are abstract, unique types of representations that are not found in non-humans. How the brain is organized to support syntactic processing is thus of neurobiological interest. Functional neuroimaging studies of the neural basis for syntactic processing have resulted in a number of theoretical positions, but the data supporting these positions is generally weak. This review presents a selective and critical review of important recent contributions to this literature. We focus on psychological methodology and interpretation of results and suggest several new approaches to the study of syntactic processing that might avoid some of the problems with existing work.