Subject motion during magnetic resonance imaging (MRI) has been problematic since its introduction as a clinical imaging modality. While sensitivity to particle motion or blood flow can be used to provide useful image contrast, bulk motion presents a considerable problem in the majority of clinical applications. It is one of the most frequent sources of artefacts. Over 30 years of research have produced numerous methods to mitigate or correct for motion artefacts, but no single method can be applied in all imaging situations. Instead, a ‘toolbox’ of methods exists, where each tool is suitable for some tasks, but not for others. This article reviews the origins of motion artefacts and presents current mitigation and correction methods. In some imaging situations, the currently available motion correction tools are highly effective; in other cases, appropriate tools still need to be developed. It seems likely that this multifaceted approach will be what eventually solves the motion sensitivity problem in MRI, rather than a single solution that is effective in all situations. This review places a strong emphasis on explaining the physics behind the occurrence of such artefacts, with the aim of aiding artefact detection and mitigation in particular clinical situations.