X-ray computer tomography (CT) is fast becoming an accepted tool within the materials science community for the acquisition of 3D images. Here the authors review the current state of the art as CT transforms from a qualitative diagnostic tool to a quantitative one. Our review considers first the image acquisition process, including the use of iterative reconstruction strategies suited to specific segmentation tasks and emerging methods that provide more insight (e.g. fast and high resolution imaging, crystallite (grain) imaging) than conventional attenuation based tomography. Methods and shortcomings of CT are examined for the quantification of 3D volumetric data to extract key topological parameters such as phase fractions, phase contiguity, and damage levels as well as density variations. As a non-destructive technique, CT is an ideal means of following structural development over time via time lapse sequences of 3D images (sometimes called 3D movies or 4D imaging). This includes information needed to optimise manufacturing processes, for example sintering or solidification, or to highlight the proclivity of specific degradation processes under service conditions, such as intergranular corrosion or fatigue crack growth. Besides the repeated application of static 3D image quantification to track such changes, digital volume correlation (DVC) and particle tracking (PT) methods are enabling the mapping of deformation in 3D over time. Finally the use of CT images is considered as the starting point for numerical modelling based on realistic microstructures, for example to predict flow through porous materials, the crystalline deformation of polycrystalline aggregates or the mechanical properties of composite materials.

X-ray computed tomography (CT) can reveal the internal details of objects in three dimensions non-destructively. In this Primer, we outline the basic principles of CT and describe the ways in which a CT scan can be acquired using X-ray tubes and synchrotron sources, including the different possible contrast modes that can be exploited. We explain the process of computationally reconstructing three-dimensional (3D) images from 2D radiographs and how to segment the 3D images for subsequent visualization and quantification. Whereas CT is widely used in medical and heavy industrial contexts at relatively low resolutions, here we focus on the application of higher resolution X-ray CT across science and engineering. We consider the application of X-ray CT to study subjects across the materials, metrology and manufacturing, engineering, food, biological, geological and palaeontological sciences. We examine how CT can be used to follow the structural evolution of materials in three dimensions in real time or in a time-lapse manner, for example to follow materials manufacturing or the in-service behaviour and degradation of manufactured components. Finally, we consider the potential for radiation damage and common sources of imaging artefacts, discuss reproducibility issues and consider future advances and opportunities.