Understanding how language networks change during childhood is important for theories of cognitive development and for identifying the neural causes of language impairment. Despite this, there is currently little systematic evidence regarding the typical developmental trajectory for language from the field of neuroimaging. We reviewed functional MRI (fMRI) studies published between 1992 and 2014, and quantified the evidence for age-related changes in localisation and lateralisation of fMRI activation in the language network (excluding the cerebellum and subcortical regions). Although age-related changes differed according to task type and input modality, we identified four consistent findings concerning the typical maturation of the language system. First, activation in core semantic processing regions increases with age. Second, activation in lower-level sensory and motor regions increases with age as activation in higher-level control regions reduces. We suggest that this reflects increased automaticity of language processing as children become more proficient. Third, the posterior cingulate cortex and precuneus (regions associated with the default mode network) show increasing attenuation across childhood and adolescence. Finally, language lateralisation is established by approximately 5 years of age. Small increases in leftward lateralisation are observed in frontal regions, but these are tightly linked to performance.