Diffraction of slow electrons is a powerful experimental tool to study the geometry and electronic structure of the surface with spatial and temporal resolution. In low-energy electron microscopy (LEEM), a rapidly developing full-field imaging technique, this strong diffraction effect is largely responsible for the image contrast observed, which calls for its quantitative understanding. In their contribution (pp. 463–477), Flege and Krasovskii review the theoretical framework of ab initio scattering theory for the interaction of slow electrons with crystalline solids as well as current experimental efforts to achieve a nanoscale characterization of multicomponent materials and related transformation processes. Exemplary intensity–voltage (I(V)) LEEM studies are described to illustrate the capabilities of the method for enhanced sample characterization and its potential in the light of future instrumental developments and current major scientific thrust areas. Experimental results for oxide model catalysts are depicted in the front cover image. Based on complex band structure (lower panel) analysis and ab initio scattering calculations, the contrast in the background image can be traced back to inhomogeneous chemical reduction of cerium oxide whereas the sphere sequence visualizes time-resolved reverse oxygen spillover phenomena in mixed ruthenium metal/oxide systems.