Accelerated imaging is highly relevant for many CMR applications as competing constraints with respect to spatiotemporal resolution and tolerable scan times are frequently posed. Three approaches, all involving data undersampling to increase scan efficiencies, are discussed in this review. Zonal imaging can be considered a niche but nevertheless has found application in coronary imaging and CMR flow measurements. Current work on parallel-transmit systems is expected to revive the interest in zonal imaging techniques. The second and main approach to speeding up CMR sequences has been parallel imaging. A wide range of CMR applications has benefited from parallel imaging with reduction factors of two to three routinely applied for functional assessment, perfusion, viability and coronary imaging. Large coil arrays, as are becoming increasingly available, are expected to support reduction factors greater than three to four in particular in combination with 3D imaging protocols. Despite these prospects, theoretical work has indicated fundamental limits of coil encoding at clinically available magnetic field strengths. In that respect, alternative approaches exploiting prior knowledge about the object being imaged as such or jointly with parallel imaging have attracted considerable attention. Five to eight-fold scan accelerations in cine and dynamic CMR applications have been reported and image quality has been found to be favorable relative to using parallel imaging alone.With all acceleration techniques, careful consideration of the limits and the trade-off between acceleration and occurrence of artifacts that may arise if these limits are breached is required. In parallel imaging the spatially varying noise has to be considered when measuring contrast- and signal-to-noise ratios. Also, temporal fidelity in images reconstructed with prior knowledge driven methods has to be studied carefully.