This talk aims to give an introduction to some of the history, theory, and numerical analysis in computed tomography (CT). Research questions centered around optimal sampling of the measured data and numerical analysis of reconstruction algorithms will be discussed as well. CT is an imaging method that produces images of the interior of opaque objects. We will focus on its original and most basic form, where the measurements are the relative attenuation of thin x-rays that pass through the object. Mathematically, such measurements give line integrals of the unknown density inside the object, and the task is then to reconstruct this density function from its line integrals. CT has found wide applications in medical diagnostics, science, and engineering.