Magnetic resonance imaging (MRI) is essential in modern medicine and has been used to visualize a variety of biological phenomena noninvasively. Recent advances in data processing have enabled accelerated undersampling of the MRI data by taking advantages of compressed sensing, which utilizes sparsity of the object. Within a few years, a variety of techniques have been introduced to deal with fast and accurate recovery of the MR images. Sparsity and low-rankedness are sought and exploited not only in the image domain but also in the frequency domain.