The processing of syntax is an ability specific to humans. The functional and structural neural network underlying this ability will be expounded, both on the basis of data from natural and artificial grammar paradigms in the mature brain. The different brain regions in the temporal, parietal and inferior frontal cortex which are involved in syntax will be described with respect to their specific contributions in the processing of syntactically complex sentences, as will the information flow between them. A model framing these data with respect to bottom-up and potential top-down processes will be presented.