Progress in the instrumentation and, in particular, in the photon sources makes it possible to implement a number of established X-ray spectroscopies in a high-lateral-resolution mode. We discuss the general trends of this field, and then we present a detailed analysis of a particular and very interesting branch: photoemission spectromicroscopy. The results include a recent world record in lateral and energy resolution, obtained by the MAXIMUM system at Wisconsin, and microimages of materials science systems as well as of neuron networks.