Extracorporeal high-intensity focused ultrasound (HIFU) is a minimally invasive therapy considered with increased interest for the ablation of small tumors in deeply located organs while sparing surrounding critical tissues. A multitude of preclinical and clinical studies have showed the feasibility of the method; however, concurrently they showed several obstacles, among which the management of respiratory motion of abdominal organs is at the forefront. The aim of this review is to describe the different methods that have been proposed for managing respiratory motion and to identify their advantages and weaknesses. First, we specify the characteristics of respiratory motion for the liver, kidneys, and pancreas and the problems it causes during HIFU planning, treatment, and monitoring. Second, we make an inventory of the preclinical and clinical approaches used to overcome the problem of organ motion. Third, we analyze their respective benefits and drawbacks to identify the remaining physical, technological, and clinical challenges. We thereby consider the outlook of motion compensation techniques and those that would be the most suitable for clinical use, particularly under magnetic resonance thermometry monitoring.