Cardiovascular magnetic resonance imaging (CVMRI) is of proven clinical value in the non-invasive imaging of cardiovascular diseases. CVMRI requires rapid image acquisition, but acquisition speed is fundamentally limited in conventional MRI. Parallel imaging provides a means for increasing acquisition speed and efficiency. However, signal-to-noise (SNR) limitations and the limited number of receiver channels available on most MR systems have in the past imposed practical constraints, which dictated the use of moderate accelerations in CVMRI. High levels of acceleration, which were unattainable previously, have become possible with many-receiver MR systems and many-element, cardiac-optimized RF-coil arrays. The resulting imaging speed improvements can be exploited in a number of ways, ranging from enhancement of spatial and temporal resolution to efficient whole heart coverage to streamlining of CVMRI work flow. In this review, examples of these strategies are provided, following an outline of the fundamentals of the highly accelerated imaging approaches employed in CVMRI. Topics discussed include basic principles of parallel imaging; key requirements for MR systems and RF-coil design; practical considerations of SNR management, supported by multi-dimensional accelerations, 3D noise averaging and high field imaging; highly accelerated clinical state-of-the art cardiovascular imaging applications spanning the range from SNR-rich to SNR-limited; and current trends and future directions.