Nanotomography is a technique of growing importance in the investigation of the shape, size, distribution and elemental composition of a wide variety of materials that are of central interest to investigators in the physical and biological sciences. Nanospatial factors often hold the key to a deeper understanding of the properties of matter at the nanoscale level. With recent advances in tomography, it is possible to achieve experimental resolution in the nanometre range, and to determine with elemental specificity the three-dimensional distribution of materials. This critical review deals principally with electron tomography, but it also outlines the power and future potential of transmission X-ray tomography, and alludes to other related techniques.