Whilst additive manufacturing allows the production of highly complex parts, X-ray computed tomography enables the holistic characterisation and measurement of such parts, including their intricate geometries and inner features that would not be accessible otherwise. This chapter explores the possibilities offered by X-ray computed tomography in the field of additive manufacturing. Fundamentals and basic principles of the tomographic techniques and systems are presented. Error sources and measurement traceability aspects are discussed. The chapter highlights the challenges and capabilities of X-ray computed tomography for several applications, ranging from characterisation of powder feedstock to measurement of final products, and from product development to process optimisation.