High Intensity Focused Ultrasound (HIFU) can be used to achieve a local temperature increase deep inside the human body in a non-invasive way. MRI guidance of the procedure allows in situ target definition. In addition, MRI can be used to provide continuous temperature mapping during HIFU for spatial and temporal control of the heating procedure and prediction of the final lesion based on the received thermal dose. Temperature mapping of mobile organs as kidney and liver is challenging, as well as real-time processing methods for feedback control of the HIFU procedure. In this paper, recent technological advances are reviewed in MR temperature mapping of these organs, in motion compensation of the HIFU beam, in intercostal HIFU sonication, and in volumetric ablation and feedback control strategies. Recent pre-clinical studies have demonstrated the feasibility of each of these novel methods. The perspectives to translate those advances into the clinic are addressed. It can be concluded that MR guided HIFU for ablation in liver and kidney appears feasible but requires further work on integration of technologically advanced methods.