Crystalline materials such as most metals, ceramics, rocks, drugs, and bones are composed of a 3D space-filling network of small crystallites r the grains. The geometry of this network governs a range of physical properties such as hardness and lifetime before failure. Our group has pursued an experimental method r 3DXRD r which for the first time enable structural characterisation of the grains in 3D. Furthermore, changes in grain morphology can be followed during typical industrial processes such as annealing or deformation. 3DXRD is based on reconstruction principles. In comparison to conventional tomography the use of higher dimensional spaces is required. The projections are subject to group symmetry and their number is inherently limited. The grains exhibit a number of geometric properties which can be utilised. Furthermore the problem at hand can be reformulated in terms of both vector-type and scalar-type reconstructions. In conjunction these effects make 3DXRD reconstruction mathematically challenging. The 3DXRD method will be presented with a few applications. The algorithms developed so far r for simplifying cases r will be summarised with focus on continuous reconstruction methods.