While a long history of neuropsychological research places language function within a primarily left-lateralized frontotemporal system, recent neuroimaging work has extended this language network to include a number of regions traditionally thought of as 'domain-general'. These include dorsal frontal, parietal, and medial temporal lobe regions known to underpin cognitive functions such as attention and memory. In this paper, we argue that these domain-general systems are not required for language processing and are instead an artefact of the tasks typically used to study language. Recent work from our lab shows that when syntactic processing - arguably the only domain-specific language function - is measured in a task-free, naturalistic manner, only the left-lateralized frontotemporal syntax system and auditory network are activated. When syntax is measured within the context of a task, several other domain-general networks come online and are functionally connected to the frontotemporal system. While we have long argued that syntactic processing does not occur in isolation but is processed in parallel with semantics and pragmatics - functions of the wider language system - our recent work makes a strong case for the domain-specificity of the frontotemporal syntax system and its autonomy from domain-general networks.