The essence of human language is its unbounded combinatory potential: Generative systems of syntax and semantics allow for the composition of an infinite range of expressions from a limited set of elementary building blocks. My research aims to characterize the representational and processing properties of this combinatory system. What are its basic computational units and how do they structurally combine? After completing a substantial body of theoretical work addressing the syntax-semantics interface for a particular subdomain of grammar (the verb phrase), I turned my research focus to characterizing the brain mechanisms responsible for the semantic combinatorics of language . The operations by which our brains build complex meanings from simpler pieces are intimately intertwined with computations building complex syntactic structures. Thus an important goal of my laboratory is to also understand the neural bases of syntactic structure building . Finally, since complex syntactic and semantic representations are, in some sense, the end product of language comprehension, being able to study them requires an understanding of the lower-level processes leading up to them. Thus in addition to studies directly targeting sentence-level semantics, my research has also addressed word-level processes such as lexical access and morphological decomposition. To monitor brain activity, the work in my lab primarily employs magnetoencephalography (MEG), which offers the best combination of temporal and spatial resolution among currently available cognitive neuroscience methods.