This review covers the theoretical background, pulse sequence considerations, practical implementations, and multitudes of applications of magnetic resonance acoustic radiation force imaging (MR-ARFI) described to date. MR-ARFI is an approach to encode tissue displacement caused by the acoustic radiation force of a focused ultrasound field into the phase of a MR image. The displacement encoding is done with motion encoding gradients (MEG) which have traditionally been added to spin echo-type and gradient recalled echo-type pulse sequences. Many different types of MEG (monopolar, bipolar, tripolar etc.) have been described and pros and cons are discussed. We further review studies investigating the safety of MR-ARFI, as well as approaches to simulate the MR-ARFI displacement. Lastly, MR-ARFI applications such as for focal spot localization, tissue stiffness interrogation following thermal ablation, trans-skull aberration correction, and simultaneous MR-ARFI and MR thermometry are discussed. EVIDENCE LEVEL: N/A TECHNICAL EFFICACY: Stage 1.