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 several novel findings: 1) the neural representation of adjective semantics observed during adjective reading is reactivated after phrase reading, with remarkable consistency, 2) a neural representation of the adjective is also present during noun presentation, but this neural representation is the reverse of that observed during adjective presentation 3) the neural representation of adjective semantics are oscillatory and entrained to alpha band frequencies. We also introduce a new method for analyzing brain image time series called Time Generalized Averaging. Taken together, these results paint a picture of information flow in the brain as phrases are read and understood.