As a person reads, the brain performs complex operations to create higher order semantic representations from individual words. While these steps are effortless for competent readers, we are only beginning to understand how the brain performs these actions. Here, we explore semantic composition using magnetoencephalography (MEG) recordings of people reading adjective-noun phrases presented one word at a time. We track the neural representation of semantic information over time, through different brain regions. Our results reveal two novel findings: 1) a neural representation of the adjective is present during noun presentation, but this neural representation is different from that observed during adjective presentation 2) the neural representation of adjective semantics observed during adjective reading is reactivated after phrase reading, with remarkable consistency. We also note that while the semantic representation of the adjective during the reading of the adjective is very distributed, the later representations are concentrated largely to temporal and frontal areas previously associated with composition. Taken together, these results paint a picture of information flow in the brain as phrases are read and understood.