We describe the use of focused ion beam sputtering to create tomographic reconstructions of objects at length scales ranging from tens of nanometers to tens of microns. This is achieved by imaging (with secondary electrons or secondary ion mass spectroscopy, SIMS) the sputtered surface at different depths in the sample. Computer interpolation of successive images then enables reconstruction of the 3D structure and chemistry. The final reconstructions typically contain several million independent voxels of data. We will describe experimental strategies for optimizing the realizable spatial resolution, for example by minimizing generation of topography arising from differential sputtering rates. We will also describe implementation of computer algorithms for interpolating between experimental images. The simplest algorithms employ linear interpolation of pixel intensities between successive images, but these techniques work well only where structures are relatively uniform along the normal to the sputtered surface. For structures with high curvature along the sputtering direction, we employ shape-based interpolation techniques (as developed for the medical tomography field) that enable complex geometrical forms to be reconstructed. Spatial resolution is defined primarily by the probe size and the lateral spread of the incident Ga ions in the sample for lateral resolution, and the implant depth for incident Ga ions and escape depth for secondary electrons/ions for vertical resolution. We have confirmed predicted resolution of order 20-30 nm by direct lateral and vertical detection of 22 nm layers in InAlP/InGaP heterostructures. Chemical sensitivities are greatly limited by the low ionization efficiency of most materials by primary Ga ions. Accordingly, we are exploring photon-based techniques for post-sample ionization of sputtered neutrals. This work is done in collaboration with A. Kubis and G. Shiflet (UVa), D. Dunn (IBM) and D. Backman (GE).