Magnetic Resonance Imaging (MRI) is an essential technology in modern medicine. However, one of its main drawbacks is the long scan time needed to localize the MR signal in space to generate an image. This review article summarizes some basic principles and recent developments in parallel imaging, a class of image reconstruction techniques for shortening scan time. First, the fundamentals of MRI data acquisition are covered, including the concepts of k-space, undersampling, and aliasing. It is demonstrated that scan time can be reduced by sampling a smaller number of phase encoding lines in k-space; however, without further processing, the resulting images will be degraded by aliasing artifacts. Nearly all modern clinical scanners acquire data from multiple independent receiver coil arrays. Parallel imaging methods exploit properties of these coil arrays to separate aliased pixels in the image domain or to estimate missing k-space data using knowledge of nearby acquired k-space points. Three parallel imaging methods-SENSE, GRAPPA, and SPIRiT-are described in detail, since they are employed clinically and form the foundation for more advanced methods. These techniques can be extended to non-Cartesian sampling patterns, where the collected k-space points do not fall on a rectangular grid. Non-Cartesian acquisitions have several beneficial properties, the most important being the appearance of incoherent aliasing artifacts. Recent advances in simultaneous multi-slice imaging are presented next, which use parallel imaging to disentangle images of several slices that have been acquired at once. Parallel imaging can also be employed to accelerate 3D MRI, in which a contiguous volume is scanned rather than sequential slices. Another class of phase-constrained parallel imaging methods takes advantage of both image magnitude and phase to achieve better reconstruction performance. Finally, some applications are presented of parallel imaging being used to accelerate MR Spectroscopic Imaging.