Ultrasonic computed tomography (UCT) is a potentially useful technique that has been explored for decades in the context of medical imaging. UCT can provide quantitative images of acoustical parameters such as speed of sound, attenuation, and density from measurements of pressure fields. Throughout the years, several algorithms that rely on different wave propagation models have been developed. In this chapter, the fundamentals of forward and inverse solvers for ultrasonic tomography will be described.