We review recent work in the application of Auger and X-ray photoelectron diffraction at high electron kinetic energies to the problem of structure determination in ultrathin epitaxial overlayers. These closely-related techniques are based on the fact that outgoing Auger and photoelectrons from single-crystal specimens undergo elastic scattering and interference from near-neighbour atoms in the vicinity of the emitter. Such coherent diffraction leads to large intensity modulations as the detected emission direction is varied with respect to the crystal axes of the specimen. The measured modulations are readily interpreted by means of model quantum mechanical scattering calculation in which atomic coordinates in the epitaxial film are systematically varied. Such analyses provide several kinds of useful information, including growth modes accompanying heteroepitaxy, structural details of alloy and compound formation, and quantitative determination of tetragonal distortion at lattice-mismatched heterointerfaces. After a discussion of experimental design and theoretical modelling, we present several case studies of heteroepitaxial growth involving dissimilar materials. In addition, we review the new subfield of Auger and photoelectron holography, and discuss the current stateof-art in both data acquisition and Fourier inversion of experimental data for directly obtaining structural parameters.