The roots of x-ray computed tomography (CT) date back to several key developments roughly 100 years old. When introduced in 1972, x-ray CT revolutionized medicine and it was recognized in 1979 by the awarding of the Nobel Prize to the scientists credited for its invention. X-ray CT is a technique for gaining knowledge of the internal structure and composition of an object using physical measurements, mathematical analysis, and computational methods. X-ray CT is used today for many medical diagnostic tests. It is also used in manufacturing and engineering for non-destructive testing of objects. This talk will cover the history of the physics, mathematics, and computer science of x-ray CT, discuss the design of modern scanners, and give example applications of x-ray CT in both medicine and manufacturing.