Hardness testing obtains material properties from small specimens via measurement of load-displacement response to an imposed indentation; it is a surface characterisation technique so, except in optically transparent materials, there is no direct observation of the assumed damage and deformation processes within the material. Three-dimensional digital image correlation ('digital volume correlation') is applied to study deformation beneath indentations, mapping the relative displacements between high-resolution synchrotron X-ray computed tomographs (0.9 μm voxel size). Two classes of material are examined: ductile aluminium-silicon carbide composite (Al-SiC) and brittle alumina (Al2O3). The measured displacements for Hertzian indentation in Al-SiC are in good agreement with an elastic-plastic finite element simulation. In alumina, radial cracking is observed beneath a Vickers indentation and the crack opening displacements are measured, in situ under load, for the first time. Potential applications are discussed of this characterization technique, which does not require resolution of microstructural features.