High intensity focused ultrasound (HIFU) is an increasingly popular physical tool with a wide range of applications in medicine. One of the drivers of this advancement is the development of ultrasound phased arrays, which, although more complex and costly than the traditional single focused bowl transducers used in earlier studies, are capable of electronically controlled dynamic focusing. Such systems not only steer a single focus without movement of the array itself, but can also generate several foci simultaneously and create focal regions with complex configurations. This book addresses the design, research and development, and medical applications of both relatively small HIFU arrays that can be inserted into body cavities (so called linear arrays) and larger two dimensional arrays for extracorporeal use. A key safety issue in the design of these arrays is to ensure that only targeted tissue is exposed to high levels of acoustic intensity and in this regard, this book highlights the advantages of designs involving spatial randomization of array elements to reduce the level of potentially dangerous grating lobes. In particular, phased arrays with a random distribution of elements are discussed and compared to regular arrays, and methods for calculating ultrasound fields generated by different phased arrays including the generation of multiple simultaneous foci and focal regions with complex geometrical shapes are presented. A detailed discussion of the influence of the dimensions, number, and shape of individual elements, errors in phase setting at the elements, and the frequency modulation of the signal on the quality of the intensity distributions produced by random arrays is included.