A hallmark of human language is that we combine lexical building blocks retrieved from memory in endless new ways. This combinatorial aspect of language is referred to as unification. Here we focus on the neurobiological infrastructure for syntactic and semantic unification. Unification is characterized by a high-speed temporal profile including both prediction and integration of retrieved lexical elements. A meta-analysis of numerous neuroimaging studies reveals a clear dorsal/ventral gradient in both left inferior frontal cortex and left posterior temporal cortex, with dorsal foci for syntactic processing and ventral foci for semantic processing. In addition to core areas for unification, further networks need to be recruited to realize language-driven communication to its full extent. One example is the theory of mind network, which allows listeners and readers to infer the intended message (speaker meaning) from the coded meaning of the linguistic utterance. This indicates that sensorimotor simulation cannot handle all of language processing.