Ion beams are now widely used to thin, shape, or cut materials on the submicrometer scale. This is possible because ions can sputter (i.e., physically remove) material from the target. Ions can also be used to image materials because the incident beam generates ion-induced secondary electrons (iSE). In both cases, the nature of the target material and the choice of the ion employed and its initial energy will determine not only how quickly the beam can thin a specimen, but also the resolution and contrast of the iSE image that is generated. Clearly, there is a need to be able to predict parameters, such as the nature, information content, and spatial resolution of the iSE image. These and other related questions have been investigated using Monte Carlo simulations. We show how the parameters defining quantities, such as depth of penetration and the energy deposited by the incident beam, or the signal yield and resolution of the iSE image, can be predicted using this approach and how these results make it possible to interpret data and optimize operating conditions.