Prior investigations of functional specialization have focused on the response profiles of particular brain regions. Given the growing emphasis on regional covariation, we propose to reframe these questions in terms of brain 'networks' (collections of regions jointly engaged by some mental process). Despite the challenges that investigations of the language network face, a network approach may prove useful in understanding the cognitive architecture of language. We propose that a language network plausibly includes a functionally specialized 'core' (brain regions that coactivate with each other during language processing) and a domain-general 'periphery' (a set of brain regions that may coactivate with the language core regions at some times but with other specialized systems at other times, depending on task demands). Framing the debate around network properties such as this may prove to be a more fruitful way to advance our understanding of the neurobiology of language.