High Intensity Focused Ultrasound (HIFU) is a non-invasive therapy for myriad potential applications for virtually any body organ and innumerable disease states. However, despite being available for many decades, the number of widely accepted, or approved applications is very limited. While many of the biological effects of ultrasound are well understood i.e. tissue hyperthermia, some are much less predictable i.e. cavitation, and some are very poorly understood at all - blood brain barrier (BBB) disruption, neuromodulation, immunomodulation etc. The use of mathematical modelling to predict the effects of HIFU for thermal ablation has facilitated the implementation for such disorders as osteoid osteoma, essential tremor, and prostate ablation. However the unpredictability or concern of unintended energy deposition has limited HIFU's application, compounded by lack of understanding of some of the biological effects - BBB opening etc. At the Centre of Image Guided Innovation and Therpeutic Interventions (CIGITI) we have explored the use of MRgFUS for bone, brain, abdomen, heart, peripheral nerve, and soft tissue tumours. Generalization of mathematical modelling for soft tissue lesions, and for the abdominal and thoracic viscera motion compensation is an important next step related to the critical important area of targeting. Developing models for the enigmatic phenomena of BBB disruption, or neuromodulation, suggests a limitless opportunity for contributions of mathematics to HIFU.