Accelerated magnetic resonance imaging techniques reduce signal acquisition time by undersampling k-space. A fundamental problem in accelerated magnetic resonance imaging is the recovery of quality images from undersampled k-space data. Current state-of-the-art recovery algorithms exploit the spatial and temporal structures in underlying images to improve the reconstruction quality. In recent years, compressed sensing theory has helped formulate mathematical principles and conditions that ensure recovery of (structured) sparse signals from undersampled, incoherent measurements. In this article, a new recovery algorithm, motion-adaptive spatio-temporal regularization, is presented that uses spatial and temporal structured sparsity of MR images in the compressed sensing framework to recover dynamic MR images from highly undersampled k-space data. In contrast to existing algorithms, our proposed algorithm models temporal sparsity using motion-adaptive linear transformations between neighboring images. The efficiency of motion-adaptive spatio-temporal regularization is demonstrated with experiments on cardiac magnetic resonance imaging for a range of reduction factors. Results are also compared with k-t FOCUSS with motion estimation and compensation—another recently proposed recovery algorithm for dynamic magnetic resonance imaging. Magn Reson Med 70:800–812, 2013. © 2012 Wiley Periodicals, Inc.