The year 2021 marks the 50th anniversary of the clinical X-ray computed tomography (CT). Over the years, CT has experienced tremendous growth enabled by both hardware advancements and software innovations. The goal of this course is to provide attendees with a fundamental understanding of the principles of CT, key design considerations and tradeoffs, technical evolutions, as well as the most recent technological and clinical advancements. The course starts with an explanation of the fundamental physics and mathematical principles of CT. Key system performance parameters and design tradeoffs are reviewed. Causes and corrections of various image artifacts are extensively discussed. Key performance parameters and their impact on clinical utilities are outlined. Given the diverse nature of the CT customers, ranging from radiologists, CT operator, hospital administrator, and patients, different ways of presenting CT images, such as volume rendering and 3D printing, are presented. The tutorial will focus on the evolution of technology and discuss basic principles, benefits, and inherent issues associated with the helical (spiral) CT, multi-slice CT, and volumetric CT. Different reconstruction approaches to combat artifacts and dose reduction, such as iterative reconstruction and more recently deep-learning based image reconstruction, are discussed. The profound impact of AI technology to the entire CT operation and design are presented. The tutorial will conclude with a discussion on dual energy and photon-counting detector. Throughout the presentation, the clinical drivers that motivated the technology development, such as coronary CT angiography and advanced stroke applications, are outlined.