Computed tomography (CT) was introduced in the early 1970s, and has since then revolutionized diagnostic imaging. Today, CT is the backbone of radiology. In this article we review different CT system design concepts. We start with an overview of the ''classic'' four generations of CT systems: the first generation head scanners relying on the ''translate-rotate'' principle, second generation scanners with a small detector array instead of a single detector, modern third generation ''rotate-rotate'' CT scanners with a detector fan wide enough to cover a whole-body scan field of view, and finally the currently abandoned fourth generation CT systems with a rotating X-ray tube and stationary detector. We present basic concepts and a short history of multidetector row CT (MDCT), illustrating its potential and limitations. Then, we introduce novel system concepts, such as CT systems with area detectors and dual source CT, that aim at solving remaining limitations of MDCT. We explain the basic system options to acquire dual energy CT data or spectrally resolved CT data. Finally, we briefly touch alternative system designs, such as electron beam CT, CT systems with inverse geometry, interior tomography CT, and phase contrast CT.