Semantic cognition brings meaning to our world – it allows us to make sense of what we see and hear, and to produce adaptive thoughts and behaviour. Since we have a wealth of information about any given concept, our store of knowledge is not sufficient for successful semantic cognition; we also need mechanisms that can steer the information that we retrieve so it suits the context or our current goals. This talk traces the neural networks that underpin this flexibility in semantic cognition. It draws on evidence from multiple methods (neuropsychology, neuroimaging, neural stimulation) to show that two interacting heteromodal networks underpin different aspects of flexibility. Regions including anterior temporal cortex and left angular gyrus respond more strongly when semantic retrieval follows highly-related concepts or multiple convergent cues; the multivariate responses in these regions correspond to context-dependent aspects of meaning. A second network centred on left inferior frontal gyrus and left posterior middle temporal gyrus is associated with controlled semantic retrieval, responding more strongly when weak associations are required or there is more competition between concepts. This semantic control network is linked to creativity and also captures context-dependent aspects of meaning; however, this network specifically shows more similar multivariate responses across trials when association strength is weak, reflecting a common controlled retrieval state when more unusual associations are the focus. Evidence from neuropsychology, fMRI and TMS suggests that this semantic control network is distinct from multiple-demand cortex which supports executive control across domains, although challenging semantic tasks recruit both networks. The semantic control network is juxtaposed between regions of default mode network that might be sufficient for the retrieval of strong semantic relationships and multiple-demand regions in the left hemisphere, suggesting that the large-scale organisation of flexible semantic cognition can be understood in terms of cortical gradients that capture systematic functional transitions that are repeated in temporal, parietal and frontal cortex.