Dynamic cardiac Magnetic Resonance Imaging (CMR) demands fast imaging techniques to obtain high spatial-resolution, large spatial-coverage and high temporal-resolution images for accurate prognosis and diagnosis. Compressed sensing, a fast imaging technique of growing importance, is making a major impact on MRI. However, the complex dynamics which include both object motions and image contrast variations encountered in dynamic CMR pose challenging tasks for CS techniques. This dissertation presents a novel CS method to accelerate dynamic CMR imaging, especially those with complex dynamics, with a motion-compensated CS method that exploits regional spatiotemporal sparsity: Block LOw-rank Sparsity with Motion-guidance (BLOSM). In Aim 1 of the dissertation, the BLOSM method was first developed and validated using retrospectively accelerated CMR data and computer simulated motion phantoms. Two CMR applications, first-pass perfusion for myocardial blood flow assessment and cine DENSE for myocardium mechanics assessment, both of which present extremely challenging tasks for CS reconstruction, were prospectively accelerated using BLOSM in this dissertation. In Aim 2, first-pass cardiac perfusion imaging was accelerated on patients with suspected heart disease. With prospective rate 4 acceleration, multi-slice high spatial resolution perfusion images were acquired. The image quality offered by BLOSM showed significant improvement over the other CS methods when respiratory motion occurred. In Aim 3, 2D cine DENSE imaging was accelerated using BLOSM. The scan time was shortened from two separate breathholds of total 28 heartbeats to one single breathhold of 8 heartbeats. BLOSM provided high image quality and the cardiac function assessed from BLOSM reconstructed images matched well with the fully-sampled reference data.