Modern rapid magnetic resonance (MR) imaging techniques have led to widespread use of the modality in cardiac imaging. Despite this progress, many MR studies suffer from image degradation due to involuntary motion during the acquisition. This review describes the type and extent of the motion of the heart due to the cardiac and respiratory cycles, which create image artifacts. Methods of eliminating or reducing the problems caused by the cardiac cycle are discussed, including electrocardiogram gating, subject-specific acquisition windows, and section tracking. Similarly, for respiratory motion of the heart, techniques such as breath holding, respiratory gating, section tracking, phase-encoding ordering, subject-specific translational models, and a range of new techniques are considered.