The technique of X-ray standing wavefield absorption applied to the determination of adsorbate structures at the solid-vacuum interface is reviewed with particular emphasis on those studies exploiting normal incidence to the Bragg scatterer planes which allows the method to be used to study adsorption structures at the surfaces of typical metal as well as semiconductor single crystals. The general theory of the XSW technique is described, as is the connection between the structural parameters obtained from the method, the so-called coherent position and coherent fraction, and the actual distribution of adsorbed atoms at the surface. Some general conclusions concerning the significance of low and high coherent fractions are drawn, with especial emphasis on adsorption at fee (111) surfaces as model systems, but considering high and low symmetry local adsorption sites, and simple and complex commensurate structures as well as incommensurate overlayer phases. Extensions of the method to obtain structural information on clean surface structures and adsorbate-induced modification of substrate surfaces, primarily concerning surface layer relaxations, are also described. The special advantages and problems of photoemission monitoring of the X-ray standing wavefield at adsorbate sites are considered, including the ability to obtain chemical state-specific as well as element-specific structural information and the special problems encountered when non-dipole effects contribute significantly to the photoemission process.