Parallel imaging has been the single biggest innovation in magnetic resonance imaging in the last decade. The use of multiple receiver coils to augment the time consuming Fourier encoding has reduced acquisition times significantly. This increase in speed comes at a time when other approaches to acquisition time reduction were reaching engineering and human limits. A brief summary of spatial encoding in MRI is followed by an introduction to the problem parallel imaging is designed to solve. There are a large number of parallel reconstruction algorithms; this article reviews a cross-section, SENSE, SMASH, g-SMASH and GRAPPA, selected to demonstrate the different approaches. Theoretical (the g-factor) and practical (coil design) limits to acquisition speed are reviewed. The practical implementation of parallel imaging is also discussed, in particular coil calibration. How to recognize potential failure modes and their associated artefacts are shown. Well-established applications including angiography, cardiac imaging and applications using echo planar imaging are reviewed and we discuss what makes a good application for parallel imaging. Finally, active research areas where parallel imaging is being used to improve data quality by repairing artefacted images are also reviewed.