A brief history of medical ultrasound imaging is given to provide a setting for illustration and comparison of new imaging techniques. These new techniques are divided into two classes, namely, transmission tomography and synthetic focus reflection tomography.The evolution of transmission tomography is presented and predictions are given for future developments such as synergistic, quantitative multiple acoustic parameter tissue imaging by solution of the wave equation. Reflection synthetic focus imaging is subdivided into two subclasses based respectively on a heuristic focusing by back projection method and a more abstract method based on inversion of a matrix which relates object and data. Those characteristics of acoustic tomography, not found in x-ray CT, are illustrated by the impedance gradient related, image cancellation artifact.