The mission of cognitive neuroscience is to represent the interaction of cognitive science and neuroscience: cognitive models of the mind guide a neuroscientific investigation of the brain bases of mental processes. In this endeavour, a cognitive model is crucial as without it, the cognitive neuroscientist does not know what to look for in the brain, what the nature of the relevant representations might be, or how the different components of a process might interact with each other. In the cognitive neuroscience of language, the interaction of theoretical models and brain research has, however, been far from ideal, especially when it comes to the study of meaning at the sentence level. Although theoretical semantics has a long history in linguistics and thus offers detailed and comprehensive models of the nature of semantic representations, these theories have had minimal impact on the brain investigation of semantic processing. In this article, we outline what a theoretically grounded cognitive neuroscience of semantics might look like and summarise our own findings regarding the neural bases of semantic composition, the basic combinatory operation that builds the complex meanings of natural language.