The current status of photoelectron and Auger-electron diffraction is reviewed, with emphasis on new directions of activity. The use of forward scattering in the study of adsorbed molecules, epitaxial overlayers, and clean surfaces is one of the most developed applications, and one that will become more powerful as higher energy resolution and perhaps spin analysis are used to resolve emitters on the basis of chemical state, position at a surface, or magnetic state. The use of larger data sets spanning a considerable fraction of the solid angle above a surface will also much enhance the structural information available, for example, in the growth of epitaxial layers or nanostructures on surfaces. Detailed fitting of experimental data to theoretical calculations based upon either single scattering or multiple scattering should also provide more rich structural information, including such parameters as substrate interlayer relaxation. Surface phase transitions in which near-surface layers become highly disordered can also be studied, with results that are complementary to those from such techniques as low-energy electron diffraction and medium-energy ion scattering. Short-range magnetic order also can be probed by somehow resolving the spin of the outgoing electrons, e.g. by using multiplet-split core levels. Valence levels also are found to exhibit core-like diffraction effects in cases for which there is somehow rather complete integration over the bands involved, e.g., through working at higher photon energies, higher temperatures and/or integrating over energy in spectra. The possibility of holographically analyzing large-scale diffraction data sets so as to directly yield three-dimensional atomic images is also promising for certain types of problems, especially adsorbates or thin overlayers. Although several types of aberrations and artifacts arise with such holographic images, a number of correction procedures appear possible, and tests of these in model calculations and for a few sets of experimental data are encouraging. Although the application of this type of analysis to multilayer substrate emission is still somewhat problematic in showing atomic images that are severely elongated, this is not necessarily true for adsorbate emission. A recent experimental and theoretical study of an adsorbate using a selected data range yields promising results. Finally, theoretical calculations indicate that it should also be possible to apply the holographic methodology to the direct imaging of short-range magnetic order.