X-ray tomographic imaging has become an indispensable tool for non-destructive three-dimensional (3D) testing of materials. The weak contrast of light elements in conventional absorption X-ray images can be overcome by X-ray phase-contrast imaging techniques. Among these, speckle-based imaging (SBI) has lately received immense attention thanks to its simple experimental setup and low requirements on the X-ray properties. SBI can be performed at laboratory sources, making it readily accessible for high-throughput use. SBI tomography delivers the quantitative 3D density distribution and simultaneously attenuation and scattering maps of the sample, providing valuable complementary information. The potential of SBI has been identified for a range of applications, such as biomedical imaging, X-ray optics testing and material characterisation. Recent advances in operational modes have further expanded the capabilities of SBI and we anticipate great interest from the materials science community, e.g. for quantitative density measurement, identification of different materials and visualisation of fibre orientation.