An important goal for the cognitive neuroscience of syntax and semantics is to move beyond general notions of “integration” when characterizing the combinatory system of language. My lab has studied the brain basis of combinatory operations for about a decade now, taking the results of formal semantics within theoretical linguistics as the model that fundamentally guides the experimentation. This work has revealed a shared combinatory network between comprehension and production comprising at least of the left anterior temporal lobe (LATL) and the ventromedial prefrontal cortex (vmPFC). In the first part of this talk, I will focus on our current understanding of the role of the LATL in combinatory processing. In the second part of the talk, I will zoom out, and consider the “hub-architecture” of the brain more generally. Across many domains of cognition, including “resting state cognition,” a relatively consistent set of highly connected network hubs keeps emerging. These include the areas implicated for composition in our work (LATL and vmPFC), but also others, such as the angular gyrus and the medial parietal cortex. In the second half of the talk, I will show recent results pertaining to the roles of the latter two in language processing. The overall picture that emerges is that when we look for the brain basis of combinatory processing in language, we find the same hubs that are implicated for integrative processing in many domains.