Motion correction in magnetic resonance imaging by real-time adjustment of the imaging pulse sequence was first proposed more than 20 years ago. Recent advances have resulted from combining real-time correction with new navigator and external tracking mechanisms capable of quantifying rigid-body motion in all 6 degrees of freedom. The technique is now often referred to as "prospective motion correction." This article describes the fundamentals of prospective motion correction and reviews the latest developments in its application to brain imaging and spectroscopy. Although emphasis is placed on the brain as the organ of interest, the same principles apply whenever the imaged object can be approximated as a rigid body. Prospective motion correction can be used with most MR sequences, so it has potential to make a large impact in clinical routine. To maximize the benefits obtained from the technique, there are, however, several challenges still to be met. These include practical implementation issues, such as obtaining tracking data with minimal delay, and more fundamental problems, such as the magnetic field distortions caused by a moving object. This review discusses these challenges and summarizes the state of the art. We hope that this work will motivate further developments in prospective motion correction and help the technique to reach its full potential.