This thesis investigated hemispheric differences in semantic cognition and their contribution to behaviour, using resting-state and task-based fMRI in conjunction with automated meta-analyses and cognitive decoding. The controlled semantic cognition framework proposes that distinct brain regions support the long-term representation of heteromodal conceptual knowledge and semantic control processes that retrieve currently-relevant aspects of knowledge. However, previous studies have not investigated whether these components have distinct patterns of lateralisation. Chapter 2 assessed intrinsic connectivity of four regions implicated in semantic cognition: anterior temporal lobe, angular gyrus, inferior frontal gyrus, and posterior middle temporal gyrus. Semantic sites in the left hemisphere showed connectivity with both control regions and default mode network, whilst their right hemisphere homotopes showed connectivity with control regions and visual and attentional systems. Semantic control regions showed the strongest lateralisation. Chapter 3 examined hemispheric specialisation of the anterior temporal lobes, strongly implicated in semantic representation. It assessed the relationship between differential intrinsic connectivity and behaviour outside the scanner on a semantic categorisation task previously shown to be sensitive to lateralisation. Graded differences in connectivity between left and right anterior temporal lobes, and from right anterior temporal cortex to the visual system related to semantic efficiency. Finally, Chapter 4 tested the specificity of the semantic control system and its relationship to domain-general control. Using a task known to engage domain-general inhibition, but introducing semantic content, this chapter yields evidence that regions implicated in semantic control are not sensitive to challenging tasks that require exercising controlled processing, and instead are specific to semantic processing. Together, these results constitute evidence for a component-process architecture in the semantic cognition system, with different patterns of lateralisation for the semantic representation and control systems. Within these systems, the results confirm the specific nature of semantic control, and fit with the graded-hub architecture of semantic representation.