Until very recently, the three-dimensionality of the material world presented numerous challenges in terms of characterization, data handling, visualization, and modeling. For this reason, 2D representation of sections, projections, or surfaces remained the mainstay of most popular imaging techniques, such as optical and electron microscopy and X-ray radiography. However, the advent of faster computers with greater memory capacity ensured that large 3D matrices can now not only be stored and manipulated efficiently, but also that advanced algorithms such as algebraic reconstruction techniques (ART) can be used to interpret redundant datasets containing multiple projections or averages across the object obtained by some suitable analytical measurement technique. These tools open up unprecedented opportunities for numerical simulation. Model formulation can be accomplished semi-automatically on the basis of microstructurally-informed 3D imaging, while model validation can be achieved by direct comparison of 3D maps of complex quantities, such as displacement vectors or strain tensor components. In this paper, we review several modalities of what can be referred to as "rich" tomography: strain tomography in the bulk of a load bearing structural component; Laue orientation tomography for nondestructive mapping of grain orientation within a polycrystal, and the use of sequences of tomographic reconstructions for digital volume correlation (DVC) analysis of in situ deformation.