Abstract: <b<Purpose:</b< Prime theories and methods of ultrasound computed tomography (UCT) will be briefly summarized in this paper. <b<Method:</b< Here, we pay most attention to transmission-mode UCT and reflection-mode UCT under the condition that scattering is neglected,and diffraction tomography. The research purposes and principles of these theories are reviewed as well as image reconstruction method. In the end, we will introduce briefly the application of inverse scattering problem in ultrasonic imaging. <b<Result:</b< Although ultrasound computed tomography has receive more and more attention in medical imaging, it is only applied successfully to some soft issue, because the theories about it have strict existence conditions, such as weak scattering, etc.